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Author : Patrick Kenneth Corn
Publisher :
ISBN 13 :
Total Pages : 422 pages
Book Rating : 4.:/5 (35 download)
Download or read book Del Pezzo Surfaces and the Brauer-Manin Obstruction written by Patrick Kenneth Corn and published by . This book was released on 2005 with total page 422 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Bianca Viray
Publisher :
ISBN 13 :
Total Pages : 76 pages
Book Rating : 4.:/5 (769 download)
Download or read book The Algebraic Brauer-Manin Obstruction on Chatelet Surfaces, Degree 4 Del Pezzo Surfaces, and Enriques Surfaces written by Bianca Viray and published by . This book was released on 2010 with total page 76 pages. Available in PDF, EPUB and Kindle. Book excerpt: We construct infinitely many Chatelet surfaces, degree 4 del Pezzo surfaces, and Enriques surfaces that are everywhere locally solvable, but have no global rational points. The lack of rational points on these surfaces is explained by an algebraic Brauer-Manin obstruction. The Enriques surfaces arise as quotients of certain K3 surfaces that are ramified double covers of a degree 4 del Pezzo surface with no rational points. We also construct an algebraic family of Chatelet surfaces over an open subscheme of P̂1_Q such that exactly 1 Q-fiber has no Q-points. This example is in stark contrast to the philosophy "geometry controls arithmetic."
Author : Jorg Jahnel
Publisher : American Mathematical Soc.
ISBN 13 : 1470418827
Total Pages : 280 pages
Book Rating : 4.4/5 (74 download)
Download or read book Brauer Groups, Tamagawa Measures, and Rational Points on Algebraic Varieties written by Jorg Jahnel and published by American Mathematical Soc.. This book was released on 2014-12-02 with total page 280 pages. Available in PDF, EPUB and Kindle. Book excerpt: The central theme of this book is the study of rational points on algebraic varieties of Fano and intermediate type--both in terms of when such points exist and, if they do, their quantitative density. The book consists of three parts. In the first part, the author discusses the concept of a height and formulates Manin's conjecture on the asymptotics of rational points on Fano varieties. The second part introduces the various versions of the Brauer group. The author explains why a Brauer class may serve as an obstruction to weak approximation or even to the Hasse principle. This part includes two sections devoted to explicit computations of the Brauer-Manin obstruction for particular types of cubic surfaces. The final part describes numerical experiments related to the Manin conjecture that were carried out by the author together with Andreas-Stephan Elsenhans. The book presents the state of the art in computational arithmetic geometry for higher-dimensional algebraic varieties and will be a valuable reference for researchers and graduate students interested in that area.
Author : Anthony Varilly
Publisher :
ISBN 13 :
Total Pages : 194 pages
Book Rating : 4.:/5 (35 download)
Download or read book Arithmetic of Del Pezzo Surfaces of Degree 1 written by Anthony Varilly and published by . This book was released on 2009 with total page 194 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Bjorn Poonen
Publisher : Springer Science & Business Media
ISBN 13 : 0817681701
Total Pages : 292 pages
Book Rating : 4.8/5 (176 download)
Download or read book Arithmetic of Higher-Dimensional Algebraic Varieties written by Bjorn Poonen and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text offers a collection of survey and research papers by leading specialists in the field documenting the current understanding of higher dimensional varieties. Recently, it has become clear that ideas from many branches of mathematics can be successfully employed in the study of rational and integral points. This book will be very valuable for researchers from these various fields who have an interest in arithmetic applications, specialists in arithmetic geometry itself, and graduate students wishing to pursue research in this area.
Author : Fedor Bogomolov
Publisher : Springer Science & Business Media
ISBN 13 : 146146482X
Total Pages : 324 pages
Book Rating : 4.4/5 (614 download)
Download or read book Birational Geometry, Rational Curves, and Arithmetic written by Fedor Bogomolov and published by Springer Science & Business Media. This book was released on 2013-05-17 with total page 324 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book features recent developments in a rapidly growing area at the interface of higher-dimensional birational geometry and arithmetic geometry. It focuses on the geometry of spaces of rational curves, with an emphasis on applications to arithmetic questions. Classically, arithmetic is the study of rational or integral solutions of diophantine equations and geometry is the study of lines and conics. From the modern standpoint, arithmetic is the study of rational and integral points on algebraic varieties over nonclosed fields. A major insight of the 20th century was that arithmetic properties of an algebraic variety are tightly linked to the geometry of rational curves on the variety and how they vary in families. This collection of solicited survey and research papers is intended to serve as an introduction for graduate students and researchers interested in entering the field, and as a source of reference for experts working on related problems. Topics that will be addressed include: birational properties such as rationality, unirationality, and rational connectedness, existence of rational curves in prescribed homology classes, cones of rational curves on rationally connected and Calabi-Yau varieties, as well as related questions within the framework of the Minimal Model Program.
Author : Boris E. Kunyavskiĭ
Publisher :
ISBN 13 :
Total Pages : 124 pages
Book Rating : 4.:/5 (44 download)
Download or read book Del Pezzo Surfaces of Degree Four written by Boris E. Kunyavskiĭ and published by . This book was released on 1989 with total page 124 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Richard Thomas
Publisher : American Mathematical Soc.
ISBN 13 : 1470435780
Total Pages : 658 pages
Book Rating : 4.4/5 (74 download)
Download or read book Algebraic Geometry: Salt Lake City 2015 written by Richard Thomas and published by American Mathematical Soc.. This book was released on 2018-06-01 with total page 658 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is Part 2 of a two-volume set. Since Oscar Zariski organized a meeting in 1954, there has been a major algebraic geometry meeting every decade: Woods Hole (1964), Arcata (1974), Bowdoin (1985), Santa Cruz (1995), and Seattle (2005). The American Mathematical Society has supported these summer institutes for over 50 years. Their proceedings volumes have been extremely influential, summarizing the state of algebraic geometry at the time and pointing to future developments. The most recent Summer Institute in Algebraic Geometry was held July 2015 at the University of Utah in Salt Lake City, sponsored by the AMS with the collaboration of the Clay Mathematics Institute. This volume includes surveys growing out of plenary lectures and seminar talks during the meeting. Some present a broad overview of their topics, while others develop a distinctive perspective on an emerging topic. Topics span both complex algebraic geometry and arithmetic questions, specifically, analytic techniques, enumerative geometry, moduli theory, derived categories, birational geometry, tropical geometry, Diophantine questions, geometric representation theory, characteristic and -adic tools, etc. The resulting articles will be important references in these areas for years to come.
Author : Jean-Louis Colliot-Thélène
Publisher : Springer Nature
ISBN 13 : 3030742482
Total Pages : 450 pages
Book Rating : 4.0/5 (37 download)
Download or read book The Brauer–Grothendieck Group written by Jean-Louis Colliot-Thélène and published by Springer Nature. This book was released on 2021-07-30 with total page 450 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph provides a systematic treatment of the Brauer group of schemes, from the foundational work of Grothendieck to recent applications in arithmetic and algebraic geometry. The importance of the cohomological Brauer group for applications to Diophantine equations and algebraic geometry was discovered soon after this group was introduced by Grothendieck. The Brauer–Manin obstruction plays a crucial role in the study of rational points on varieties over global fields. The birational invariance of the Brauer group was recently used in a novel way to establish the irrationality of many new classes of algebraic varieties. The book covers the vast theory underpinning these and other applications. Intended as an introduction to cohomological methods in algebraic geometry, most of the book is accessible to readers with a knowledge of algebra, algebraic geometry and algebraic number theory at graduate level. Much of the more advanced material is not readily available in book form elsewhere; notably, de Jong’s proof of Gabber’s theorem, the specialisation method and applications of the Brauer group to rationality questions, an in-depth study of the Brauer–Manin obstruction, and proof of the finiteness theorem for the Brauer group of abelian varieties and K3 surfaces over finitely generated fields. The book surveys recent work but also gives detailed proofs of basic theorems, maintaining a balance between general theory and concrete examples. Over half a century after Grothendieck's foundational seminars on the topic, The Brauer–Grothendieck Group is a treatise that fills a longstanding gap in the literature, providing researchers, including research students, with a valuable reference on a central object of algebraic and arithmetic geometry.
Author : Clay Mathematics Institute. Summer School
Publisher : American Mathematical Soc.
ISBN 13 : 0821844768
Total Pages : 570 pages
Book Rating : 4.8/5 (218 download)
Download or read book Arithmetic Geometry written by Clay Mathematics Institute. Summer School and published by American Mathematical Soc.. This book was released on 2009 with total page 570 pages. Available in PDF, EPUB and Kindle. Book excerpt: Based on survey lectures given at the 2006 Clay Summer School on Arithmetic Geometry at the Mathematics Institute of the University of Gottingen, this tile is intended for graduate students and recent PhD's. It introduces readers to modern techniques and conjectures at the interface of number theory and algebraic geometry.
Author : Ivan Arzhantsev
Publisher : Cambridge University Press
ISBN 13 : 1107024625
Total Pages : 539 pages
Book Rating : 4.1/5 (7 download)
Download or read book Cox Rings written by Ivan Arzhantsev and published by Cambridge University Press. This book was released on 2015 with total page 539 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a largely self-contained introduction to Cox rings and their applications in algebraic and arithmetic geometry.
Author : Alexei N. Skorobogatov
Publisher : Cambridge University Press
ISBN 13 : 1107245265
Total Pages : 470 pages
Book Rating : 4.1/5 (72 download)
Download or read book Torsors, Étale Homotopy and Applications to Rational Points written by Alexei N. Skorobogatov and published by Cambridge University Press. This book was released on 2013-04-18 with total page 470 pages. Available in PDF, EPUB and Kindle. Book excerpt: Torsors, also known as principal bundles or principal homogeneous spaces, are ubiquitous in mathematics. The purpose of this book is to present expository lecture notes and cutting-edge research papers on the theory and applications of torsors and étale homotopy, all written from different perspectives by leading experts. Part one of the book contains lecture notes on recent uses of torsors in geometric invariant theory and representation theory, plus an introduction to the étale homotopy theory of Artin and Mazur. Part two of the book features a milestone paper on the étale homotopy approach to the arithmetic of rational points. Furthermore, the reader will find a collection of research articles on algebraic groups and homogeneous spaces, rational and K3 surfaces, geometric invariant theory, rational points, descent and the Brauer–Manin obstruction. Together, these give a state-of-the-art view of a broad area at the crossroads of number theory and algebraic geometry.
Author : Bjorn Poonen
Publisher : American Mathematical Soc.
ISBN 13 : 1470437732
Total Pages : 358 pages
Book Rating : 4.4/5 (74 download)
Download or read book Rational Points on Varieties written by Bjorn Poonen and published by American Mathematical Soc.. This book was released on 2017-12-13 with total page 358 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.
Author : Alexei Skorobogatov
Publisher : Cambridge University Press
ISBN 13 : 0521802377
Total Pages : 197 pages
Book Rating : 4.5/5 (218 download)
Download or read book Torsors and Rational Points written by Alexei Skorobogatov and published by Cambridge University Press. This book was released on 2001-07-05 with total page 197 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book, first published in 2001, is a complete and coherent exposition of the theory and applications of torsors to rational points.
Author : Bjorn Poonen
Publisher : American Mathematical Society
ISBN 13 : 1470474581
Total Pages : 357 pages
Book Rating : 4.4/5 (74 download)
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
Author : Yuri Tschinkel
Publisher : Universitätsverlag Göttingen
ISBN 13 : 3930457709
Total Pages : 200 pages
Book Rating : 4.9/5 (34 download)
Download or read book Mathematisches Institut Georg-august-universität Göttingen, Seminars Summer Term 2004 written by Yuri Tschinkel and published by Universitätsverlag Göttingen. This book was released on 2004 with total page 200 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains lecture notes from the seminars [alpha]Number Theory", [alpha]Algebraic Geometry" and [alpha]Geometric methods in representation theory" which took place at the Mathematics Institute of the University of Göttingen during the Summer Term 2004. Most contributions report on recent work by the authors.
Author : Wolf P. Barth
Publisher : Walter de Gruyter
ISBN 13 : 3110889439
Total Pages : 353 pages
Book Rating : 4.1/5 (18 download)
Download or read book Abelian Varieties written by Wolf P. Barth and published by Walter de Gruyter. This book was released on 2011-06-24 with total page 353 pages. Available in PDF, EPUB and Kindle. Book excerpt: The series is aimed specifically at publishing peer reviewed reviews and contributions presented at workshops and conferences. Each volume is associated with a particular conference, symposium or workshop. These events cover various topics within pure and applied mathematics and provide up-to-date coverage of new developments, methods and applications.
