Variations On A Theorem Of Tate

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Variations on a Theorem of Tate

Stefan Patrikis
Variations on a Theorem of Tate Book PDF

Author : Stefan Patrikis
Publisher : American Mathematical Soc.
Page : 156 pages
File Size : 54,9 Mb
Release : 2019-04-10
Category : Algebraic number theory
ISBN : 9781470435400

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Variations on a Theorem of Tate by Stefan Patrikis Pdf

Let F be a number field. These notes explore Galois-theoretic, automorphic, and motivic analogues and refinements of Tate's basic result that continuous projective representations Gal(F¯¯¯¯/F)→PGLn(C) lift to GLn(C). The author takes special interest in the interaction of this result with algebraicity (for automorphic representations) and geometricity (in the sense of Fontaine-Mazur). On the motivic side, the author studies refinements and generalizations of the classical Kuga-Satake construction. Some auxiliary results touch on: possible infinity-types of algebraic automorphic representations; comparison of the automorphic and Galois “Tannakian formalisms” monodromy (independence-of-ℓ) questions for abstract Galois representations.

Mumford-Tate Groups and Domains

Mark Green,Phillip A. Griffiths,Matt Kerr
Mumford Tate Groups and Domains Book PDF

Author : Mark Green,Phillip A. Griffiths,Matt Kerr
Publisher : Princeton University Press
Page : 298 pages
File Size : 48,6 Mb
Release : 2012-04-22
Category : Mathematics
ISBN : 9780691154244

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Mumford-Tate Groups and Domains by Mark Green,Phillip A. Griffiths,Matt Kerr Pdf

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.

Frobenius Manifolds

Claus Hertling,Matilde Marcolli
Frobenius Manifolds Book PDF

Author : Claus Hertling,Matilde Marcolli
Publisher : Springer Science & Business Media
Page : 384 pages
File Size : 52,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783322802361

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Frobenius Manifolds by Claus Hertling,Matilde Marcolli Pdf

Quantum cohomology, the theory of Frobenius manifolds and the relations to integrable systems are flourishing areas since the early 90's. An activity was organized at the Max-Planck-Institute for Mathematics in Bonn, with the purpose of bringing together the main experts in these areas. This volume originates from this activity and presents the state of the art in the subject.

Motives

Anonim
Motives Book PDF

Author : Anonim
Publisher : American Mathematical Soc.
Page : 694 pages
File Size : 47,5 Mb
Release : 1994-02-28
Category : Mathematics
ISBN : 9780821827987

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Motives by Anonim Pdf

'Motives' were introduced in the mid-1960s by Grothendieck to explain the analogies among the various cohomology theories for algebraic varieties, and to play the role of the missing rational cohomology. This work contains the texts of the lectures presented at the AMS-IMS-SIAM Joint Summer Research Conference on Motives, held in Seattle, in 1991.

Motives

Uwe Jannsen,Jean-pierre Serre,Steven Kleiman
Motives Book PDF

Author : Uwe Jannsen,Jean-pierre Serre,Steven Kleiman
Publisher : American Mathematical Soc.
Page : 696 pages
File Size : 55,5 Mb
Release : 1994-02-28
Category : Mathematics
ISBN : 0821827995

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Motives by Uwe Jannsen,Jean-pierre Serre,Steven Kleiman Pdf

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. These two volumes contain 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.

Mumford-Tate Groups and Domains

Mark Green,Phillip Griffiths,Matthew D. Kerr
Mumford Tate Groups and Domains Book PDF

Author : Mark Green,Phillip Griffiths,Matthew D. Kerr
Publisher : Princeton University Press
Page : 299 pages
File Size : 44,7 Mb
Release : 2012
Category : Mathematics
ISBN : 9780691154251

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Mumford-Tate Groups and Domains by Mark Green,Phillip Griffiths,Matthew D. Kerr Pdf

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.

Arithmetic Duality Theorems

J. S. Milne
Arithmetic Duality Theorems Book PDF

Author : J. S. Milne
Publisher : Unknown
Page : 440 pages
File Size : 43,5 Mb
Release : 1986
Category : Mathematics
ISBN : UOM:39076000806617

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Arithmetic Duality Theorems by J. S. Milne Pdf

Here, published for the first time, are the complete proofs of the fundamental arithmetic duality theorems that have come to play an increasingly important role in number theory and arithmetic geometry. The text covers these theorems in Galois cohomology, ,tale cohomology, and flat cohomology and addresses applications in the above areas. The writing is expository and the book will serve as an invaluable reference text as well as an excellent introduction to the subject.

Number Theory

Jean-Marie De Koninck,Claude Levesque
Number Theory Book PDF

Author : Jean-Marie De Koninck,Claude Levesque
Publisher : Walter de Gruyter
Page : 1038 pages
File Size : 49,9 Mb
Release : 1989
Category : Mathematics
ISBN : 3110117916

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Number Theory by Jean-Marie De Koninck,Claude Levesque Pdf

Monumental proceedings (very handsomely produced) of a major international conference. The book contains 74 refereed articles which, apart from a few survey papers of peculiar interest, are mostly research papers (63 in English, 11 in French). The topics covered reflect the full diversity of the current trends and activities in modern number theory: elementary, algebraic and analytic number theory; constructive (computational) number theory; elliptic curves and modular forms; arithmetical geometry; transcendence; quadratic forms; coding theory. (NW) Annotation copyrighted by Book News, Inc., Portland, OR

Recent Advances in Hodge Theory

Matt Kerr,Gregory Pearlstein
Recent Advances in Hodge Theory Book PDF

Author : Matt Kerr,Gregory Pearlstein
Publisher : Cambridge University Press
Page : 533 pages
File Size : 40,5 Mb
Release : 2016-02-04
Category : Mathematics
ISBN : 9781107546295

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Recent Advances in Hodge Theory by Matt Kerr,Gregory Pearlstein Pdf

Combines cutting-edge research and expository articles in Hodge theory. An essential reference for graduate students and researchers.

Number Theory and Applications

S.D. Adhikari,B. Ramakrishnan
Number Theory and Applications Book PDF

Author : S.D. Adhikari,B. Ramakrishnan
Publisher : Springer
Page : 285 pages
File Size : 54,8 Mb
Release : 2009-06-15
Category : Mathematics
ISBN : 9789386279460

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Number Theory and Applications by S.D. Adhikari,B. Ramakrishnan Pdf

This collection of articles contains the proceedings of the two international conferences (on Number Theory and Cryptography) held at the Harish - Chandra Research Institute. In recent years the interest in number theory has increased due to its applications in areas like error-correcting codes and cryptography. These proceedings contain papers in various areas of number theory, such as combinatorial, algebraic, analytic and transcendental aspects, arithmetic algebraic geometry, as well as graph theory and cryptography. While some papers do contain new results, several of the papers are expository articles that mention open questions, which will be useful to young researchers.

Collected Works of John Tate

Barry Mazur,Jean-Pierre Serre
Collected Works of John Tate Book PDF

Author : Barry Mazur,Jean-Pierre Serre
Publisher : American Mathematical Soc.
Page : 716 pages
File Size : 40,9 Mb
Release : 2016-12-13
Category : Algebraic fields
ISBN : 9780821890929

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Collected Works of John Tate by Barry Mazur,Jean-Pierre Serre Pdf

In these volumes, a reader will find all of John Tate's published mathematical papers—spanning more than six decades—enriched by new comments made by the author. Included also is a selection of his letters. His letters give us a close view of how he works and of his ideas in process of formation.

Hodge Theory, Complex Geometry, and Representation Theory

Robert S. Doran,Greg Friedman,Scott Nollet
Hodge Theory Complex Geometry and Representation Theory Book PDF

Author : Robert S. Doran,Greg Friedman,Scott Nollet
Publisher : American Mathematical Soc.
Page : 330 pages
File Size : 43,6 Mb
Release : 2014
Category : Mathematics
ISBN : 9780821894156

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Hodge Theory, Complex Geometry, and Representation Theory by Robert S. Doran,Greg Friedman,Scott Nollet Pdf

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.

Algebraic Geometry and Number Theory

Hussein Mourtada,Celal Cem Sarıoğlu,Christophe Soulé,Ayberk Zeytin
Algebraic Geometry and Number Theory Book PDF

Author : Hussein Mourtada,Celal Cem Sarıoğlu,Christophe Soulé,Ayberk Zeytin
Publisher : Birkhäuser
Page : 232 pages
File Size : 51,9 Mb
Release : 2017-05-07
Category : Mathematics
ISBN : 9783319477794

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Algebraic Geometry and Number Theory by Hussein Mourtada,Celal Cem Sarıoğlu,Christophe Soulé,Ayberk Zeytin Pdf

This lecture notes volume presents significant contributions from the “Algebraic Geometry and Number Theory” Summer School, held at Galatasaray University, Istanbul, June 2-13, 2014. It addresses subjects ranging from Arakelov geometry and Iwasawa theory to classical projective geometry, birational geometry and equivariant cohomology. Its main aim is to introduce these contemporary research topics to graduate students who plan to specialize in the area of algebraic geometry and/or number theory. All contributions combine main concepts and techniques with motivating examples and illustrative problems for the covered subjects. Naturally, the book will also be of interest to researchers working in algebraic geometry, number theory and related fields.

Abelian l-Adic Representations and Elliptic Curves

Jean-Pierre Serre
Abelian l Adic Representations and Elliptic Curves Book PDF

Author : Jean-Pierre Serre
Publisher : CRC Press
Page : 203 pages
File Size : 47,5 Mb
Release : 1997-11-15
Category : Mathematics
ISBN : 9781439863862

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Abelian l-Adic Representations and Elliptic Curves by Jean-Pierre Serre Pdf

This classic book contains an introduction to systems of l-adic representations, a topic of great importance in number theory and algebraic geometry, as reflected by the spectacular recent developments on the Taniyama-Weil conjecture and Fermat's Last Theorem. The initial chapters are devoted to the Abelian case (complex multiplication), where one

Hodge Theory, Complex Geometry, and Representation Theory

Mark Green, Phillip Griffiths,Matt Kerr
Hodge Theory Complex Geometry and Representation Theory Book PDF

Author : Mark Green, Phillip Griffiths,Matt Kerr
Publisher : American Mathematical Soc.
Page : 314 pages
File Size : 52,7 Mb
Release : 2013-11-05
Category : Mathematics
ISBN : 9781470410124

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Hodge Theory, Complex Geometry, and Representation Theory by Mark Green, Phillip Griffiths,Matt Kerr Pdf

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.