Mumford Tate Groups And Domains

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Mumford-Tate Groups and Domains

Author : Mark Green
Publisher : Princeton University Press
ISBN 13 : 1400842735
Total Pages : 298 pages
Book Rating : 4.4/5 (8 download)

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Book Synopsis Mumford-Tate Groups and Domains by : Mark Green

Download or read book Mumford-Tate Groups and Domains written by Mark Green and published by Princeton University Press. This book was released on 2012-04-22 with total page 298 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mumford-Tate groups are the fundamental symmetry groups of Hodge theory, a subject which rests at the center of contemporary complex algebraic geometry. This book is the first comprehensive exploration of Mumford-Tate groups and domains. Containing basic theory and a wealth of new views and results, it will become an essential resource for graduate students and researchers. Although Mumford-Tate groups can be defined for general structures, their theory and use to date has mainly been in the classical case of abelian varieties. While the book does examine this area, it focuses on the nonclassical case. The general theory turns out to be very rich, such as in the unexpected connections of finite dimensional and infinite dimensional representation theory of real, semisimple Lie groups. The authors give the complete classification of Hodge representations, a topic that should become a standard in the finite-dimensional representation theory of noncompact, real, semisimple Lie groups. They also indicate that in the future, a connection seems ready to be made between Lie groups that admit discrete series representations and the study of automorphic cohomology on quotients of Mumford-Tate domains by arithmetic groups. Bringing together complex geometry, representation theory, and arithmetic, this book opens up a fresh perspective on an important subject.

Period Mappings and Period Domains

Author : James Carlson
Publisher : Cambridge University Press
ISBN 13 : 1108422624
Total Pages : 577 pages
Book Rating : 4.1/5 (84 download)

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Book Synopsis Period Mappings and Period Domains by : James Carlson

Download or read book Period Mappings and Period Domains written by James Carlson and published by Cambridge University Press. This book was released on 2017-08-24 with total page 577 pages. Available in PDF, EPUB and Kindle. Book excerpt: An introduction to Griffiths' theory of period maps and domains, focused on algebraic, group-theoretic and differential geometric aspects.

Hodge Theory, Complex Geometry, and Representation Theory

Author : Mark Green
Publisher : American Mathematical Soc.
ISBN 13 : 1470410125
Total Pages : 314 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Hodge Theory, Complex Geometry, and Representation Theory by : Mark Green

Download or read book Hodge Theory, Complex Geometry, and Representation Theory written by Mark Green and published by American Mathematical Soc.. This book was released on 2013-11-05 with total page 314 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph presents topics in Hodge theory and representation theory, two of the most active and important areas in contemporary mathematics. The underlying theme is the use of complex geometry to understand the two subjects and their relationships to one another--an approach that is complementary to what is in the literature. Finite-dimensional representation theory and complex geometry enter via the concept of Hodge representations and Hodge domains. Infinite-dimensional representation theory, specifically the discrete series and their limits, enters through the realization of these representations through complex geometry as pioneered by Schmid, and in the subsequent description of automorphic cohomology. For the latter topic, of particular importance is the recent work of Carayol that potentially introduces a new perspective in arithmetic automorphic representation theory. The present work gives a treatment of Carayol's work, and some extensions of it, set in a general complex geometric framework. Additional subjects include a description of the relationship between limiting mixed Hodge structures and the boundary orbit structure of Hodge domains, a general treatment of the correspondence spaces that are used to construct Penrose transforms and selected other topics from the recent literature. A co-publication of the AMS and CBMS.

Hodge Theory, Complex Geometry, and Representation Theory

Author : Robert S. Doran
Publisher : American Mathematical Soc.
ISBN 13 : 0821894153
Total Pages : 330 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Hodge Theory, Complex Geometry, and Representation Theory by : Robert S. Doran

Download or read book Hodge Theory, Complex Geometry, and Representation Theory written by Robert S. Doran and published by American Mathematical Soc.. This book was released on 2014 with total page 330 pages. Available in PDF, EPUB and Kindle. Book excerpt: Contains carefully written expository and research articles. Expository papers include discussions of Noether-Lefschetz theory, algebraicity of Hodge loci, and the representation theory of SL2(R). Research articles concern the Hodge conjecture, Harish-Chandra modules, mirror symmetry, Hodge representations of Q-algebraic groups, and compactifications, distributions, and quotients of period domains.

Calabi-Yau Varieties: Arithmetic, Geometry and Physics

Author : Radu Laza
Publisher : Springer
ISBN 13 : 1493928309
Total Pages : 542 pages
Book Rating : 4.4/5 (939 download)

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Book Synopsis Calabi-Yau Varieties: Arithmetic, Geometry and Physics by : Radu Laza

Download or read book Calabi-Yau Varieties: Arithmetic, Geometry and Physics written by Radu Laza and published by Springer. This book was released on 2015-08-27 with total page 542 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents a lively introduction to the rapidly developing and vast research areas surrounding Calabi–Yau varieties and string theory. With its coverage of the various perspectives of a wide area of topics such as Hodge theory, Gross–Siebert program, moduli problems, toric approach, and arithmetic aspects, the book gives a comprehensive overview of the current streams of mathematical research in the area. The contributions in this book are based on lectures that took place during workshops with the following thematic titles: “Modular Forms Around String Theory,” “Enumerative Geometry and Calabi–Yau Varieties,” “Physics Around Mirror Symmetry,” “Hodge Theory in String Theory.” The book is ideal for graduate students and researchers learning about Calabi–Yau varieties as well as physics students and string theorists who wish to learn the mathematics behind these varieties.

The Abel Prize 2008-2012

Author : Helge Holden
Publisher : Springer Science & Business Media
ISBN 13 : 3642394493
Total Pages : 561 pages
Book Rating : 4.6/5 (423 download)

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Book Synopsis The Abel Prize 2008-2012 by : Helge Holden

Download or read book The Abel Prize 2008-2012 written by Helge Holden and published by Springer Science & Business Media. This book was released on 2014-01-21 with total page 561 pages. Available in PDF, EPUB and Kindle. Book excerpt: Covering the years 2008-2012, this book profiles the life and work of recent winners of the Abel Prize: · John G. Thompson and Jacques Tits, 2008 · Mikhail Gromov, 2009 · John T. Tate Jr., 2010 · John W. Milnor, 2011 · Endre Szemerédi, 2012. The profiles feature autobiographical information as well as a description of each mathematician's work. In addition, each profile contains a complete bibliography, a curriculum vitae, as well as photos — old and new. As an added feature, interviews with the Laureates are presented on an accompanying web site (http://extras.springer.com/). The book also presents a history of the Abel Prize written by the historian Kim Helsvig, and includes a facsimile of a letter from Niels Henrik Abel, which is transcribed, translated into English, and placed into historical perspective by Christian Skau. This book follows on The Abel Prize: 2003-2007, The First Five Years (Springer, 2010), which profiles the work of the first Abel Prize winners.

Arithmetic Geometry of Logarithmic Pairs and Hyperbolicity of Moduli Spaces

Author : Marc-Hubert Nicole
Publisher : Springer Nature
ISBN 13 : 3030498646
Total Pages : 247 pages
Book Rating : 4.0/5 (34 download)

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Book Synopsis Arithmetic Geometry of Logarithmic Pairs and Hyperbolicity of Moduli Spaces by : Marc-Hubert Nicole

Download or read book Arithmetic Geometry of Logarithmic Pairs and Hyperbolicity of Moduli Spaces written by Marc-Hubert Nicole and published by Springer Nature. This book was released on 2020-10-31 with total page 247 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook introduces exciting new developments and cutting-edge results on the theme of hyperbolicity. Written by leading experts in their respective fields, the chapters stem from mini-courses given alongside three workshops that took place in Montréal between 2018 and 2019. Each chapter is self-contained, including an overview of preliminaries for each respective topic. This approach captures the spirit of the original lectures, which prepared graduate students and those new to the field for the technical talks in the program. The four chapters turn the spotlight on the following pivotal themes: The basic notions of o-minimal geometry, which build to the proof of the Ax–Schanuel conjecture for variations of Hodge structures; A broad introduction to the theory of orbifold pairs and Campana's conjectures, with a special emphasis on the arithmetic perspective; A systematic presentation and comparison between different notions of hyperbolicity, as an introduction to the Lang–Vojta conjectures in the projective case; An exploration of hyperbolicity and the Lang–Vojta conjectures in the general case of quasi-projective varieties. Arithmetic Geometry of Logarithmic Pairs and Hyperbolicity of Moduli Spaces is an ideal resource for graduate students and researchers in number theory, complex algebraic geometry, and arithmetic geometry. A basic course in algebraic geometry is assumed, along with some familiarity with the vocabulary of algebraic number theory.

Special Values of Automorphic Cohomology Classes

Author : Mark Green
Publisher : American Mathematical Soc.
ISBN 13 : 0821898574
Total Pages : 158 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Special Values of Automorphic Cohomology Classes by : Mark Green

Download or read book Special Values of Automorphic Cohomology Classes written by Mark Green and published by American Mathematical Soc.. This book was released on 2014-08-12 with total page 158 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors study the complex geometry and coherent cohomology of nonclassical Mumford-Tate domains and their quotients by discrete groups. Their focus throughout is on the domains which occur as open -orbits in the flag varieties for and , regarded as classifying spaces for Hodge structures of weight three. In the context provided by these basic examples, the authors formulate and illustrate the general method by which correspondence spaces give rise to Penrose transforms between the cohomologies of distinct such orbits with coefficients in homogeneous line bundles.

Hodge Theory

Author : Eduardo Cattani
Publisher : Princeton University Press
ISBN 13 : 0691161348
Total Pages : 607 pages
Book Rating : 4.6/5 (911 download)

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Book Synopsis Hodge Theory by : Eduardo Cattani

Download or read book Hodge Theory written by Eduardo Cattani and published by Princeton University Press. This book was released on 2014-07-21 with total page 607 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a comprehensive and up-to-date introduction to Hodge theory—one of the central and most vibrant areas of contemporary mathematics—from leading specialists on the subject. The topics range from the basic topology of algebraic varieties to the study of variations of mixed Hodge structure and the Hodge theory of maps. Of particular interest is the study of algebraic cycles, including the Hodge and Bloch-Beilinson Conjectures. Based on lectures delivered at the 2010 Summer School on Hodge Theory at the ICTP in Trieste, Italy, the book is intended for a broad group of students and researchers. The exposition is as accessible as possible and doesn't require a deep background. At the same time, the book presents some topics at the forefront of current research. The book is divided between introductory and advanced lectures. The introductory lectures address Kähler manifolds, variations of Hodge structure, mixed Hodge structures, the Hodge theory of maps, period domains and period mappings, algebraic cycles (up to and including the Bloch-Beilinson conjecture) and Chow groups, sheaf cohomology, and a new treatment of Grothendieck’s algebraic de Rham theorem. The advanced lectures address a Hodge-theoretic perspective on Shimura varieties, the spread philosophy in the study of algebraic cycles, absolute Hodge classes (including a new, self-contained proof of Deligne’s theorem on absolute Hodge cycles), and variation of mixed Hodge structures. The contributors include Patrick Brosnan, James Carlson, Eduardo Cattani, François Charles, Mark Andrea de Cataldo, Fouad El Zein, Mark L. Green, Phillip A. Griffiths, Matt Kerr, Lê Dũng Tráng, Luca Migliorini, Jacob P. Murre, Christian Schnell, and Loring W. Tu.

Surveys on Recent Developments in Algebraic Geometry

Author : Izzet Coskun
Publisher : American Mathematical Soc.
ISBN 13 : 1470435578
Total Pages : 386 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Surveys on Recent Developments in Algebraic Geometry by : Izzet Coskun

Download or read book Surveys on Recent Developments in Algebraic Geometry written by Izzet Coskun and published by American Mathematical Soc.. This book was released on 2017-07-12 with total page 386 pages. Available in PDF, EPUB and Kindle. Book excerpt: The algebraic geometry community has a tradition of running a summer research institute every ten years. During these influential meetings a large number of mathematicians from around the world convene to overview the developments of the past decade and to outline the most fundamental and far-reaching problems for the next. The meeting is preceded by a Bootcamp aimed at graduate students and young researchers. This volume collects ten surveys that grew out of the Bootcamp, held July 6–10, 2015, at University of Utah, Salt Lake City, Utah. These papers give succinct and thorough introductions to some of the most important and exciting developments in algebraic geometry in the last decade. Included are descriptions of the striking advances in the Minimal Model Program, moduli spaces, derived categories, Bridgeland stability, motivic homotopy theory, methods in characteristic and Hodge theory. Surveys contain many examples, exercises and open problems, which will make this volume an invaluable and enduring resource for researchers looking for new directions.

Cyclic Coverings, Calabi-Yau Manifolds and Complex Multiplication

Author : Christian Rohde
Publisher : Springer
ISBN 13 : 3642006396
Total Pages : 234 pages
Book Rating : 4.6/5 (42 download)

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Book Synopsis Cyclic Coverings, Calabi-Yau Manifolds and Complex Multiplication by : Christian Rohde

Download or read book Cyclic Coverings, Calabi-Yau Manifolds and Complex Multiplication written by Christian Rohde and published by Springer. This book was released on 2009-06-12 with total page 234 pages. Available in PDF, EPUB and Kindle. Book excerpt: Calabi-Yau manifolds have been an object of extensive research during the last two decades. One of the reasons is the importance of Calabi-Yau 3-manifolds in modern physics - notably string theory. An interesting class of Calabi-Yau manifolds is given by those with complex multiplication (CM). Calabi-Yau manifolds with CM are also of interest in theoretical physics, e. g. in connection with mirror symmetry and black hole attractors. It is the main aim of this book to construct families of Calabi-Yau 3-manifolds with dense sets of ?bers with complex multiplication. Most - amples in this book are constructed using families of curves with dense sets of ?bers with CM. The contents of this book can roughly be divided into two parts. The ?rst six chapters deal with families of curves with dense sets of CM ?bers and introduce the necessary theoretical background. This includes among other things several aspects of Hodge theory and Shimura varieties. Using the ?rst part, families of Calabi-Yau 3-manifolds with dense sets of ?bers withCM are constructed in the remaining ?ve chapters. In the appendix one ?nds examples of Calabi-Yau 3-manifolds with complex mul- plication which are not necessarily ?bers of a family with a dense set ofCM ?bers. The author hopes to have succeeded in writing a readable book that can also be used by non-specialists.

Recent Advances in Hodge Theory

Author : Matt Kerr
Publisher : Cambridge University Press
ISBN 13 : 110754629X
Total Pages : 533 pages
Book Rating : 4.1/5 (75 download)

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Book Synopsis Recent Advances in Hodge Theory by : Matt Kerr

Download or read book Recent Advances in Hodge Theory written by Matt Kerr and published by Cambridge University Press. This book was released on 2016-02-04 with total page 533 pages. Available in PDF, EPUB and Kindle. Book excerpt: Combines cutting-edge research and expository articles in Hodge theory. An essential reference for graduate students and researchers.

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.

Annales de l'Institut Fourier

Author :
Publisher :
ISBN 13 :
Total Pages : 940 pages
Book Rating : 4.:/5 (312 download)

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Book Synopsis Annales de l'Institut Fourier by :

Download or read book Annales de l'Institut Fourier written by and published by . This book was released on 2014 with total page 940 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Mumford-Tate Groups and Domains

Author : Mark Green
Publisher : Annals of Mathematics Studies
ISBN 13 : 9780691154251
Total Pages : 302 pages
Book Rating : 4.1/5 (542 download)

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Book Synopsis Mumford-Tate Groups and Domains by : Mark Green

Download or read book Mumford-Tate Groups and Domains written by Mark Green and published by Annals of Mathematics Studies. This book was released on 2012 with total page 302 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mumford-Tate groups are the fundamental symmetry groups of Hodge theory, a subject which rests at the center of contemporary complex algebraic geometry. This book is the first comprehensive exploration of Mumford-Tate groups and domains. Containing basic theory and a wealth of new views and results, it will become an essential resource for graduate students and researchers. Although Mumford-Tate groups can be defined for general structures, their theory and use to date has mainly been in the classical case of abelian varieties. While the book does examine this area, it focuses on the nonclassical case. The general theory turns out to be very rich, such as in the unexpected connections of finite dimensional and infinite dimensional representation theory of real, semisimple Lie groups. The authors give the complete classification of Hodge representations, a topic that should become a standard in the finite-dimensional representation theory of noncompact, real, semisimple Lie groups. They also indicate that in the future, a connection seems ready to be made between Lie groups that admit discrete series representations and the study of automorphic cohomology on quotients of Mumford-Tate domains by arithmetic groups. Bringing together complex geometry, representation theory, and arithmetic, this book opens up a fresh perspective on an important subject.

Representations of Algebraic Groups

Author : Jens Carsten Jantzen
Publisher : American Mathematical Soc.
ISBN 13 : 082184377X
Total Pages : 594 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Representations of Algebraic Groups by : Jens Carsten Jantzen

Download or read book Representations of Algebraic Groups written by Jens Carsten Jantzen and published by American Mathematical Soc.. This book was released on 2003 with total page 594 pages. Available in PDF, EPUB and Kindle. Book excerpt: Gives an introduction to the general theory of representations of algebraic group schemes. This title deals with representation theory of reductive algebraic groups and includes topics such as the description of simple modules, vanishing theorems, Borel-Bott-Weil theorem and Weyl's character formula, and Schubert schemes and lne bundles on them.

The Brauer–Grothendieck Group

Author : Jean-Louis Colliot-Thélène
Publisher : Springer Nature
ISBN 13 : 3030742482
Total Pages : 450 pages
Book Rating : 4.0/5 (37 download)

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Book Synopsis The Brauer–Grothendieck Group by : Jean-Louis Colliot-Thélène

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.