Galois Representations In Arithmetic Algebraic Geometry

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Galois Representations And Arithmetic Algebraic Geometry

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Author : Yasutaka Ihara
language : en
Publisher: Kinokuniya Company Limited
Release Date : 1987

Galois Representations And Arithmetic Algebraic Geometry written by Yasutaka Ihara and has been published by Kinokuniya Company Limited this book supported file pdf, txt, epub, kindle and other format this book has been release on 1987 with Mathematics categories.

Galois Representations In Arithmetic Algebraic Geometry

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Author : Scholl/Taylor
language : en
Publisher:
Release Date : 1999

Galois Representations In Arithmetic Algebraic Geometry written by Scholl/Taylor and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999 with categories.

Arithmetic Algebraic Geometry

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Author : Brian David Conrad
language : en
Publisher: American Mathematical Soc.
Release Date :

Arithmetic Algebraic Geometry written by Brian David Conrad and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on with Mathematics categories.

The articles in this volume are expanded versions of lectures delivered at the Graduate Summer School and at the Mentoring Program for Women in Mathematics held at the Institute for Advanced Study/Park City Mathematics Institute. The theme of the program was arithmetic algebraic geometry. The choice of lecture topics was heavily influenced by the recent spectacular work of Wiles on modular elliptic curves and Fermat's Last Theorem. The main emphasis of the articles in the volume is on elliptic curves, Galois representations, and modular forms. One lecture series offers an introduction to these objects. The others discuss selected recent results, current research, and open problems and conjectures. The book would be a suitable text for an advanced graduate topics course in arithmetic algebraic geometry.

Galois Representations And Arithmetic Algebraic Geometry

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Author : Yasutaka Ihara
language : en
Publisher: Kinokuniya Company Limited
Release Date : 1987

Galois Representations And Arithmetic Algebraic Geometry written by Yasutaka Ihara and has been published by Kinokuniya Company Limited this book supported file pdf, txt, epub, kindle and other format this book has been release on 1987 with Mathematics categories.

Galois Representations And Arithmetic Algebraic Geometry

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Author : Yasutaka Ihara
language : en
Publisher:
Release Date : 2018

Galois Representations And Arithmetic Algebraic Geometry written by Yasutaka Ihara and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018 with categories.

Arithmetic Fundamental Groups And Noncommutative Algebra

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Author : Michael D. Fried
language : en
Publisher: American Mathematical Soc.
Release Date : 2002

Arithmetic Fundamental Groups And Noncommutative Algebra written by Michael D. Fried and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002 with Mathematics categories.

The arithmetic and geometry of moduli spaces and their fundamental groups are a very active research area. This book offers a complete overview of developments made over the last decade. The papers in this volume examine the geometry of moduli spaces of curves with a function on them. The main players in Part 1 are the absolute Galois group $G {\mathbb Q $ of the algebraic numbers and its close relatives. By analyzing how $G {\mathbb Q $ acts on fundamental groups defined by Hurwitz moduli problems, the authors achieve a grand generalization of Serre's program from the 1960s. Papers in Part 2 apply $\theta$-functions and configuration spaces to the study of fundamental groups over positive characteristic fields. In this section, several authors use Grothendieck's famous lifting results to give extensions to wildly ramified covers. Properties of the fundamental groups have brought collaborations between geometers and group theorists. Several Part 3 papers investigate new versions of the genus 0 problem. In particular, this includes results severely limiting possible monodromy groups of sphere covers. Finally, Part 4 papers treat Deligne's theory of Tannakian categories and arithmetic versions of the Kodaira-Spencer map. This volume is geared toward graduate students and research mathematicians interested in arithmetic algebraic geometry.

The Geometric And Arithmetic Volume Of Shimura Varieties Of Orthogonal Type

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Author : Fritz Hörmann
language : en
Publisher: American Mathematical Society
Release Date : 2014-11-05

The Geometric And Arithmetic Volume Of Shimura Varieties Of Orthogonal Type written by Fritz Hörmann and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-11-05 with Mathematics categories.

This book outlines a functorial theory of integral models of (mixed) Shimura varieties and of their toroidal compactifications, for odd primes of good reduction. This is the integral version, developed in the author's thesis, of the theory invented by Deligne and Pink in the rational case. In addition, the author develops a theory of arithmetic Chern classes of integral automorphic vector bundles with singular metrics using the work of Burgos, Kramer and Kühn. The main application is calculating arithmetic volumes or "heights" of Shimura varieties of orthogonal type using Borcherds' famous modular forms with their striking product formula--an idea due to Bruinier-Burgos-Kühn and Kudla. This should be seen as an Arakelov analogue of the classical calculation of volumes of orthogonal locally symmetric spaces by Siegel and Weil. In the latter theory, the volumes are related to special values of (normalized) Siegel Eisenstein series. In this book, it is proved that the Arakelov analogues are related to special derivatives of such Eisenstein series. This result gives substantial evidence in the direction of Kudla's conjectures in arbitrary dimensions. The validity of the full set of conjectures of Kudla, in turn, would give a conceptual proof and far-reaching generalizations of the work of Gross and Zagier on the Birch and Swinnerton-Dyer conjecture. Titles in this series are co-published with the Centre de Recherches Mathématiques.

Surveys In Geometry And Number Theory

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Author : Nicholas Young
language : en
Publisher: Cambridge University Press
Release Date : 2007-01-18

Surveys In Geometry And Number Theory written by Nicholas Young and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-01-18 with Mathematics categories.

A collection of survey articles by leading young researchers, showcasing the vitality of Russian mathematics.

Recent Perspectives In Random Matrix Theory And Number Theory

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Author : F. Mezzadri
language : en
Publisher: Cambridge University Press
Release Date : 2005-06-21

Recent Perspectives In Random Matrix Theory And Number Theory written by F. Mezzadri and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-06-21 with Mathematics categories.

Provides a grounding in random matrix techniques applied to analytic number theory.

Triangulated Categories

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Author : Thorsten Holm
language : en
Publisher: Cambridge University Press
Release Date : 2010-06-24

Triangulated Categories written by Thorsten Holm and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-06-24 with Mathematics categories.

Over the last few decades triangulated categories have become increasingly important, to the extent that they can now be viewed as a unifying theory underlying major parts of modern mathematics. This 2010 collection of survey articles, written by leading experts, covers fundamental aspects of triangulated categories, as well as applications in algebraic geometry, representation theory, commutative algebra, microlocal analysis and algebraic topology. These self-contained articles are a useful introduction for graduate students entering the field and a valuable reference for experts.