The Weil Conjectures

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Weil Conjectures, Perverse Sheaves and l-adic Fourier Transform

Author : Reinhardt Kiehl
Publisher : Springer Science & Business Media
ISBN 13 : 3662045761
Total Pages : 382 pages
Book Rating : 4.6/5 (62 download)

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Book Synopsis Weil Conjectures, Perverse Sheaves and l-adic Fourier Transform by : Reinhardt Kiehl

Download or read book Weil Conjectures, Perverse Sheaves and l-adic Fourier Transform written by Reinhardt Kiehl and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 382 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors describe the important generalization of the original Weil conjectures, as given by P. Deligne in his fundamental paper "La conjecture de Weil II". The authors follow the important and beautiful methods of Laumon and Brylinski which lead to a simplification of Deligne's theory. Deligne's work is closely related to the sheaf theoretic theory of perverse sheaves. In this framework Deligne's results on global weights and his notion of purity of complexes obtain a satisfactory and final form. Therefore the authors include the complete theory of middle perverse sheaves. In this part, the l-adic Fourier transform is introduced as a technique providing natural and simple proofs. To round things off, there are three chapters with significant applications of these theories.

Etale Cohomology and the Weil Conjecture

Author : Eberhard Freitag
Publisher : Springer Science & Business Media
ISBN 13 : 3662025418
Total Pages : 336 pages
Book Rating : 4.6/5 (62 download)

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Book Synopsis Etale Cohomology and the Weil Conjecture by : Eberhard Freitag

Download or read book Etale Cohomology and the Weil Conjecture written by Eberhard Freitag and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 336 pages. Available in PDF, EPUB and Kindle. Book excerpt: Some years ago a conference on l-adic cohomology in Oberwolfach was held with the aim of reaching an understanding of Deligne's proof of the Weil conjec tures. For the convenience of the speakers the present authors - who were also the organisers of that meeting - prepared short notes containing the central definitions and ideas of the proofs. The unexpected interest for these notes and the various suggestions to publish them encouraged us to work somewhat more on them and fill out the gaps. Our aim was to develop the theory in as self contained and as short a manner as possible. We intended especially to provide a complete introduction to etale and l-adic cohomology theory including the monodromy theory of Lefschetz pencils. Of course, all the central ideas are due to the people who created the theory, especially Grothendieck and Deligne. The main references are the SGA-notes [64-69]. With the kind permission of Professor J. A. Dieudonne we have included in the book that finally resulted his excellent notes on the history of the Weil conjectures, as a second introduction. Our original notes were written in German. However, we finally followed the recommendation made variously to publish the book in English. We had the good fortune that Professor W. Waterhouse and his wife Betty agreed to translate our manuscript. We want to thank them very warmly for their willing involvement in such a tedious task. We are very grateful to the staff of Springer-Verlag for their careful work.

Weil's Conjecture for Function Fields

Author : Dennis Gaitsgory
Publisher : Princeton University Press
ISBN 13 : 0691184437
Total Pages : 320 pages
Book Rating : 4.6/5 (911 download)

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Book Synopsis Weil's Conjecture for Function Fields by : Dennis Gaitsgory

Download or read book Weil's Conjecture for Function Fields written by Dennis Gaitsgory and published by Princeton University Press. This book was released on 2019-02-19 with total page 320 pages. Available in PDF, EPUB and Kindle. Book excerpt: A central concern of number theory is the study of local-to-global principles, which describe the behavior of a global field K in terms of the behavior of various completions of K. This book looks at a specific example of a local-to-global principle: Weil’s conjecture on the Tamagawa number of a semisimple algebraic group G over K. In the case where K is the function field of an algebraic curve X, this conjecture counts the number of G-bundles on X (global information) in terms of the reduction of G at the points of X (local information). The goal of this book is to give a conceptual proof of Weil’s conjecture, based on the geometry of the moduli stack of G-bundles. Inspired by ideas from algebraic topology, it introduces a theory of factorization homology in the setting l-adic sheaves. Using this theory, Dennis Gaitsgory and Jacob Lurie articulate a different local-to-global principle: a product formula that expresses the cohomology of the moduli stack of G-bundles (a global object) as a tensor product of local factors. Using a version of the Grothendieck-Lefschetz trace formula, Gaitsgory and Lurie show that this product formula implies Weil’s conjecture. The proof of the product formula will appear in a sequel volume.

Zeta and L-Functions of Varieties and Motives

Author : Bruno Kahn
Publisher : Cambridge University Press
ISBN 13 : 1108574912
Total Pages : 217 pages
Book Rating : 4.1/5 (85 download)

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Book Synopsis Zeta and L-Functions of Varieties and Motives by : Bruno Kahn

Download or read book Zeta and L-Functions of Varieties and Motives written by Bruno Kahn and published by Cambridge University Press. This book was released on 2020-05-07 with total page 217 pages. Available in PDF, EPUB and Kindle. Book excerpt: The amount of mathematics invented for number-theoretic reasons is impressive. It includes much of complex analysis, the re-foundation of algebraic geometry on commutative algebra, group cohomology, homological algebra, and the theory of motives. Zeta and L-functions sit at the meeting point of all these theories and have played a profound role in shaping the evolution of number theory. This book presents a big picture of zeta and L-functions and the complex theories surrounding them, combining standard material with results and perspectives that are not made explicit elsewhere in the literature. Particular attention is paid to the development of the ideas surrounding zeta and L-functions, using quotes from original sources and comments throughout the book, pointing the reader towards the relevant history. Based on an advanced course given at Jussieu in 2013, it is an ideal introduction for graduate students and researchers to this fascinating story.

Geometry In Advanced Pure Mathematics

Author : Bullett Shaun
Publisher : World Scientific
ISBN 13 : 1786341093
Total Pages : 236 pages
Book Rating : 4.7/5 (863 download)

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Book Synopsis Geometry In Advanced Pure Mathematics by : Bullett Shaun

Download or read book Geometry In Advanced Pure Mathematics written by Bullett Shaun and published by World Scientific. This book was released on 2017-03-07 with total page 236 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book leads readers from a basic foundation to an advanced level understanding of geometry in advanced pure mathematics. Chapter by chapter, readers will be led from a foundation level understanding to advanced level understanding. This is the perfect text for graduate or PhD mathematical-science students looking for support in algebraic geometry, geometric group theory, modular group, holomorphic dynamics and hyperbolic geometry, syzygies and minimal resolutions, and minimal surfaces. Geometry in Advanced Pure Mathematics is the fourth volume of the LTCC Advanced Mathematics Series. This series is the first to provide advanced introductions to mathematical science topics to advanced students of mathematics. Editor the three joint heads of the London Taught Course Centre for PhD Students in the Mathematical Sciences (LTCC), each book supports readers in broadening their mathematical knowledge outside of their immediate research disciplines while also covering specialized key areas.

The Local Langlands Conjecture for GL(2)

Author : Colin J. Bushnell
Publisher : Springer Science & Business Media
ISBN 13 : 354031511X
Total Pages : 352 pages
Book Rating : 4.5/5 (43 download)

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Book Synopsis The Local Langlands Conjecture for GL(2) by : Colin J. Bushnell

Download or read book The Local Langlands Conjecture for GL(2) written by Colin J. Bushnell and published by Springer Science & Business Media. This book was released on 2006-08-29 with total page 352 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Local Langlands Conjecture for GL(2) contributes an unprecedented text to the so-called Langlands theory. It is an ambitious research program of already 40 years and gives a complete and self-contained proof of the Langlands conjecture in the case n=2. It is aimed at graduate students and at researchers in related fields. It presupposes no special knowledge beyond the beginnings of the representation theory of finite groups and the structure theory of local fields.

The Geometry of Schemes

Author : David Eisenbud
Publisher : Springer Science & Business Media
ISBN 13 : 0387226397
Total Pages : 340 pages
Book Rating : 4.3/5 (872 download)

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Book Synopsis The Geometry of Schemes by : David Eisenbud

Download or read book The Geometry of Schemes written by David Eisenbud and published by Springer Science & Business Media. This book was released on 2006-04-06 with total page 340 pages. Available in PDF, EPUB and Kindle. Book excerpt: Grothendieck’s beautiful theory of schemes permeates modern algebraic geometry and underlies its applications to number theory, physics, and applied mathematics. This simple account of that theory emphasizes and explains the universal geometric concepts behind the definitions. In the book, concepts are illustrated with fundamental examples, and explicit calculations show how the constructions of scheme theory are carried out in practice.

Motives

Author : Uwe Jannsen
Publisher : American Mathematical Soc.
ISBN 13 : 0821827987
Total Pages : 676 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Motives by : Uwe Jannsen

Download or read book Motives written by Uwe Jannsen and published by American Mathematical Soc.. This book was released on 1994 with total page 676 pages. Available in PDF, EPUB and Kindle. Book excerpt: Motives were introduced in the mid-1960s by Grothendieck to explain the analogies among the various cohomology theories for algebraic varieties, to play the role of the missing rational cohomology, and to provide a blueprint for proving Weil's conjectures about the zeta function of a variety over a finite field. Over the last ten years or so, researchers in various areas--Hodge theory, algebraic $K$-theory, polylogarithms, automorphic forms, $L$-functions, $\ell$-adic representations, trigonometric sums, and algebraic cycles--have discovered that an enlarged (and in part conjectural) theory of ``mixed'' motives indicates and explains phenomena appearing in each area. Thus the theory holds the potential of enriching and unifying these areas. This is the second of two volumes containing the revised texts of nearly all the lectures presented at the AMS-IMS-SIAM Joint Summer Research Conference on Motives, held in Seattle, in 1991. A number of related works are also included, making for a total of forty-seven papers, from general introductions to specialized surveys to research papers.

The Apprenticeship of a Mathematician

Author : Andre Weil
Publisher : Birkhäuser
ISBN 13 : 3034886349
Total Pages : 195 pages
Book Rating : 4.0/5 (348 download)

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Book Synopsis The Apprenticeship of a Mathematician by : Andre Weil

Download or read book The Apprenticeship of a Mathematician written by Andre Weil and published by Birkhäuser. This book was released on 2012-12-06 with total page 195 pages. Available in PDF, EPUB and Kindle. Book excerpt: From reviews: "Extremely readable... rare testimony of a period of the history of 20th century mathematics. Includes very interesting recollections on the author's participation in the formation of the Bourbaki Group, tells of his meetings and conversations with leading mathematicians, reflects his views on mathematics. The book describes an extraordinary career of an exceptional man and mathematicians. Strongly recommended to specialists as well as to the general public." --EMS Newsletter (1992)

The Subversive Simone Weil

Author : Robert Zaretsky
Publisher : University of Chicago Press
ISBN 13 : 0226826600
Total Pages : 192 pages
Book Rating : 4.2/5 (268 download)

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Book Synopsis The Subversive Simone Weil by : Robert Zaretsky

Download or read book The Subversive Simone Weil written by Robert Zaretsky and published by University of Chicago Press. This book was released on 2023-04-05 with total page 192 pages. Available in PDF, EPUB and Kindle. Book excerpt: Known as the “patron saint of all outsiders,” Simone Weil (1909–43) was one of the twentieth century’s most remarkable thinkers, a philosopher who truly lived by her political and ethical ideals. In a short life framed by the two world wars, Weil taught philosophy to lycée students and organized union workers, fought alongside anarchists during the Spanish Civil War and labored alongside workers on assembly lines, joined the Free French movement in London and died in despair because she was not sent to France to help the Resistance. Though Weil published little during her life, after her death, thanks largely to the efforts of Albert Camus, hundreds of pages of her manuscripts were published to critical and popular acclaim. While many seekers have been attracted to Weil’s religious thought, Robert Zaretsky gives us a different Weil, exploring her insights into politics and ethics, and showing us a new side of Weil that balances her contradictions—the rigorous rationalist who also had her own brand of Catholic mysticism; the revolutionary with a soft spot for anarchism yet who believed in the hierarchy of labor; and the humanitarian who emphasized human needs and obligations over human rights. Reflecting on the relationship between thought and action in Weil’s life, The Subversive Simone Weil honors the complexity of Weil’s thought and speaks to why it matters and continues to fascinate readers today.

Rational Points on Varieties

Author : Bjorn Poonen
Publisher : American Mathematical Society
ISBN 13 : 1470474581
Total Pages : 357 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Rational Points on Varieties by : Bjorn Poonen

Download or read book Rational Points on Varieties written by Bjorn Poonen and published by American Mathematical Society. This book was released on 2023-08-10 with total page 357 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is motivated by the problem of determining the set of rational points on a variety, but its true goal is to equip readers with a broad range of tools essential for current research in algebraic geometry and number theory. The book is unconventional in that it provides concise accounts of many topics instead of a comprehensive account of just one—this is intentionally designed to bring readers up to speed rapidly. Among the topics included are Brauer groups, faithfully flat descent, algebraic groups, torsors, étale and fppf cohomology, the Weil conjectures, and the Brauer-Manin and descent obstructions. A final chapter applies all these to study the arithmetic of surfaces. The down-to-earth explanations and the over 100 exercises make the book suitable for use as a graduate-level textbook, but even experts will appreciate having a single source covering many aspects of geometry over an unrestricted ground field and containing some material that cannot be found elsewhere. The origins of arithmetic (or Diophantine) geometry can be traced back to antiquity, and it remains a lively and wide research domain up to our days. The book by Bjorn Poonen, a leading expert in the field, opens doors to this vast field for many readers with different experiences and backgrounds. It leads through various algebraic geometric constructions towards its central subject: obstructions to existence of rational points. —Yuri Manin, Max-Planck-Institute, Bonn It is clear that my mathematical life would have been very different if a book like this had been around at the time I was a student. —Hendrik Lenstra, University Leiden Understanding rational points on arbitrary algebraic varieties is the ultimate challenge. We have conjectures but few results. Poonen's book, with its mixture of basic constructions and openings into current research, will attract new generations to the Queen of Mathematics. —Jean-Louis Colliot-Thélène, Université Paris-Sud A beautiful subject, handled by a master. —Joseph Silverman, Brown University

Lectures on K3 Surfaces

Author : Daniel Huybrechts
Publisher : Cambridge University Press
ISBN 13 : 1316797252
Total Pages : 499 pages
Book Rating : 4.3/5 (167 download)

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Book Synopsis Lectures on K3 Surfaces by : Daniel Huybrechts

Download or read book Lectures on K3 Surfaces written by Daniel Huybrechts and published by Cambridge University Press. This book was released on 2016-09-26 with total page 499 pages. Available in PDF, EPUB and Kindle. Book excerpt: K3 surfaces are central objects in modern algebraic geometry. This book examines this important class of Calabi–Yau manifolds from various perspectives in eighteen self-contained chapters. It starts with the basics and guides the reader to recent breakthroughs, such as the proof of the Tate conjecture for K3 surfaces and structural results on Chow groups. Powerful general techniques are introduced to study the many facets of K3 surfaces, including arithmetic, homological, and differential geometric aspects. In this context, the book covers Hodge structures, moduli spaces, periods, derived categories, birational techniques, Chow rings, and deformation theory. Famous open conjectures, for example the conjectures of Calabi, Weil, and Artin–Tate, are discussed in general and for K3 surfaces in particular, and each chapter ends with questions and open problems. Based on lectures at the advanced graduate level, this book is suitable for courses and as a reference for researchers.

Mathematics for Human Flourishing

Author : Francis Su
Publisher : Yale University Press
ISBN 13 : 0300237138
Total Pages : 287 pages
Book Rating : 4.3/5 (2 download)

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Book Synopsis Mathematics for Human Flourishing by : Francis Su

Download or read book Mathematics for Human Flourishing written by Francis Su and published by Yale University Press. This book was released on 2020-01-07 with total page 287 pages. Available in PDF, EPUB and Kindle. Book excerpt: "The ancient Greeks argued that the best life was filled with beauty, truth, justice, play and love. The mathematician Francis Su knows just where to find them."--Kevin Hartnett, Quanta Magazine" This is perhaps the most important mathematics book of our time. Francis Su shows mathematics is an experience of the mind and, most important, of the heart."--James Tanton, Global Math Project For mathematician Francis Su, a society without mathematical affection is like a city without concerts, parks, or museums. To miss out on mathematics is to live without experiencing some of humanity's most beautiful ideas. In this profound book, written for a wide audience but especially for those disenchanted by their past experiences, an award-winning mathematician and educator weaves parables, puzzles, and personal reflections to show how mathematics meets basic human desires--such as for play, beauty, freedom, justice, and love--and cultivates virtues essential for human flourishing. These desires and virtues, and the stories told here, reveal how mathematics is intimately tied to being human. Some lessons emerge from those who have struggled, including philosopher Simone Weil, whose own mathematical contributions were overshadowed by her brother's, and Christopher Jackson, who discovered mathematics as an inmate in a federal prison. Christopher's letters to the author appear throughout the book and show how this intellectual pursuit can--and must--be open to all.

Curves and Abelian Varieties

Author : Valery Alexeev
Publisher : American Mathematical Soc.
ISBN 13 : 9780821857939
Total Pages : 292 pages
Book Rating : 4.8/5 (579 download)

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Book Synopsis Curves and Abelian Varieties by : Valery Alexeev

Download or read book Curves and Abelian Varieties written by Valery Alexeev and published by American Mathematical Soc.. This book was released on 2008-08-15 with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is devoted to recent progress in the study of curves and abelian varieties. It discusses both classical aspects of this deep and beautiful subject as well as two important new developments, tropical geometry and the theory of log schemes. In addition to original research articles, this book contains three surveys devoted to singularities of theta divisors, of compactified Jacobians of singular curves, and of ``strange duality'' among moduli spaces of vector bundles on algebraic varieties.

The Genesis of the Langlands Program

Author : Julia Mueller
Publisher : Cambridge University Press
ISBN 13 : 1108710948
Total Pages : 451 pages
Book Rating : 4.1/5 (87 download)

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Book Synopsis The Genesis of the Langlands Program by : Julia Mueller

Download or read book The Genesis of the Langlands Program written by Julia Mueller and published by Cambridge University Press. This book was released on 2021-08-05 with total page 451 pages. Available in PDF, EPUB and Kindle. Book excerpt: A step-by-step guide to Langlands' early work leading up the Langlands Program for mathematicians and advanced students.

All the Houses

Author : Karen Olsson
Publisher : Farrar, Straus and Giroux
ISBN 13 : 0374714193
Total Pages : 416 pages
Book Rating : 4.3/5 (747 download)

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Book Synopsis All the Houses by : Karen Olsson

Download or read book All the Houses written by Karen Olsson and published by Farrar, Straus and Giroux. This book was released on 2015-11-03 with total page 416 pages. Available in PDF, EPUB and Kindle. Book excerpt: A bittersweet, biting, sharply observed family drama from the author of Waterloo After her father has a heart attack and subsequent surgery, Helen Atherton returns to her hometown of Washington, D.C., to help take care of him and, perhaps more honestly, herself. She's been living in Los Angeles, trying to work in Hollywood, slowly spiraling into a depression fueled by hours spent watching C-SPAN-her obsession with politics a holdover from a childhood interrupted by her father's involvement in the Iran-Contra scandal. "I don't know whether to think of him as a coconspirator or a complicit bystander or just someone who was in the wrong place at the wrong time." Though the rest of the world has forgotten that scandal, the Atherton family never quite recovered. While living with her father in her childhood home, Helen tries to piece together the political moves that pulled her family apart. All the Houses is, at its heart, a father-daughter story. With razor-sharp prose, an alluring objectivity, and a dry sense of humor, Karen Olsson writes about the shape-shifting of our family relationships when outside forces work their way in-how Washington turns people into unnatural versions of themselves, how problematic and overbearing sisters can be, and how familial nostalgia that sets in during early adulthood can prove counterproductive to actually becoming an adult.

p-adic Numbers, p-adic Analysis, and Zeta-Functions

Author : Neal Koblitz
Publisher : Springer Science & Business Media
ISBN 13 : 1461211123
Total Pages : 163 pages
Book Rating : 4.4/5 (612 download)

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Book Synopsis p-adic Numbers, p-adic Analysis, and Zeta-Functions by : Neal Koblitz

Download or read book p-adic Numbers, p-adic Analysis, and Zeta-Functions written by Neal Koblitz and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 163 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first edition of this work has become the standard introduction to the theory of p-adic numbers at both the advanced undergraduate and beginning graduate level. This second edition includes a deeper treatment of p-adic functions in Ch. 4 to include the Iwasawa logarithm and the p-adic gamma-function, the rearrangement and addition of some exercises, the inclusion of an extensive appendix of answers and hints to the exercises, as well as numerous clarifications.