Galois Representations And 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 Algebraic Geometry
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Author : G., van der Geer
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Arithmetic Algebraic Geometry written by G., van der Geer and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
Arithmetic algebraic geometry is in a fascinating stage of growth, providing a rich variety of applications of new tools to both old and new problems. Representative of these recent developments is the notion of Arakelov geometry, a way of "completing" a variety over the ring of integers of a number field by adding fibres over the Archimedean places. Another is the appearance of the relations between arithmetic geometry and Nevanlinna theory, or more precisely between diophantine approximation theory and the value distribution theory of holomorphic maps. Inspired by these exciting developments, the editors organized a meeting at Texel in 1989 and invited a number of mathematicians to write papers for this volume. Some of these papers were presented at the meeting; others arose from the discussions that took place. They were all chosen for their quality and relevance to the application of algebraic geometry to arithmetic problems. Topics include: arithmetic surfaces, Chjerm functors, modular curves and modular varieties, elliptic curves, Kolyvagin’s work, K-theory and Galois representations. Besides the research papers, there is a letter of Parshin and a paper of Zagier with is interpretations of the Birch-Swinnerton-Dyer Conjecture. Research mathematicians and graduate students in algebraic geometry and number theory will find a valuable and lively view of the field in this state-of-the-art selection.
Computational Aspects Of Modular Forms And Galois Representations
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Author : Bas Edixhoven
language : en
Publisher: Princeton University Press
Release Date : 2011-06-20
Computational Aspects Of Modular Forms And Galois Representations written by Bas Edixhoven and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-06-20 with Mathematics categories.
Modular forms are tremendously important in various areas of mathematics, from number theory and algebraic geometry to combinatorics and lattices. Their Fourier coefficients, with Ramanujan's tau-function as a typical example, have deep arithmetic significance. Prior to this book, the fastest known algorithms for computing these Fourier coefficients took exponential time, except in some special cases. The case of elliptic curves (Schoof's algorithm) was at the birth of elliptic curve cryptography around 1985. This book gives an algorithm for computing coefficients of modular forms of level one in polynomial time. For example, Ramanujan's tau of a prime number p can be computed in time bounded by a fixed power of the logarithm of p. Such fast computation of Fourier coefficients is itself based on the main result of the book: the computation, in polynomial time, of Galois representations over finite fields attached to modular forms by the Langlands program. Because these Galois representations typically have a nonsolvable image, this result is a major step forward from explicit class field theory, and it could be described as the start of the explicit Langlands program. The computation of the Galois representations uses their realization, following Shimura and Deligne, in the torsion subgroup of Jacobian varieties of modular curves. The main challenge is then to perform the necessary computations in time polynomial in the dimension of these highly nonlinear algebraic varieties. Exact computations involving systems of polynomial equations in many variables take exponential time. This is avoided by numerical approximations with a precision that suffices to derive exact results from them. Bounds for the required precision--in other words, bounds for the height of the rational numbers that describe the Galois representation to be computed--are obtained from Arakelov theory. Two types of approximations are treated: one using complex uniformization and another one using geometry over finite fields. The book begins with a concise and concrete introduction that makes its accessible to readers without an extensive background in arithmetic geometry. And the book includes a chapter that describes actual computations.
Galois Teichmu Ller Theory And Arithmetic Geometry
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Author : 中村博昭
language : en
Publisher: Advanced Studies in Pure Mathe
Release Date : 2012-10
Galois Teichmu Ller Theory And Arithmetic Geometry written by 中村博昭 and has been published by Advanced Studies in Pure Mathe this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-10 with Mathematics categories.
From the 1980's, Grothendieck's "Esquisse d'un Programme" triggered tremendous developments in number theory and arithmetic geometry, extending from the studies of anabelian geometry and related Galois representations to those of polylogarithms and multiple zeta values, motives, rational points on arithmetic varieties, and effectiveness questions in arithmetic geometry. The present volume collects twenty-four articles written by speakers (and their coauthors) of two international meetings focused on the above themes held in Kyoto in October 2010. It includes both survey articles and research papers which provide useful information about this area of investigation.Published by Mathematical Society of Japan and distributed by World Scientific Publishing Co. for all markets except North America
The Eigenbook
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Author : Joël Bellaïche
language : en
Publisher: Springer Nature
Release Date : 2021-08-11
The Eigenbook written by Joël Bellaïche and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-08-11 with Mathematics categories.
This book discusses the p-adic modular forms, the eigencurve that parameterize them, and the p-adic L-functions one can associate to them. These theories and their generalizations to automorphic forms for group of higher ranks are of fundamental importance in number theory. For graduate students and newcomers to this field, the book provides a solid introduction to this highly active area of research. For experts, it will offer the convenience of collecting into one place foundational definitions and theorems with complete and self-contained proofs. Written in an engaging and educational style, the book also includes exercises and provides their solution.
Abelian L Adic Representations And Elliptic Curves
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Author : Jean-Pierre Serre
language : en
Publisher: CRC Press
Release Date : 1997-11-15
Abelian L Adic Representations And Elliptic Curves written by Jean-Pierre Serre and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997-11-15 with Mathematics categories.
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