Lmsst 24 Lectures On Elliptic Curves

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Lmsst 24 Lectures On Elliptic Curves

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Author : J. W. S. Cassels
language : en
Publisher: Cambridge University Press
Release Date : 1991-11-21

Lmsst 24 Lectures On Elliptic Curves written by J. W. S. Cassels 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 1991-11-21 with Mathematics categories.

A self-contained introductory text for beginning graduate students that is contemporary in approach without ignoring historical matters.

Number Theory And Algebraic Geometry

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Author : Miles Reid
language : en
Publisher: Cambridge University Press
Release Date : 2003

Number Theory And Algebraic Geometry written by Miles Reid 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 2003 with Mathematics categories.

Sir Peter Swinnerton-Dyer's mathematical career encompasses more than 60 years' work of amazing creativity. This volume provides contemporary insight into several subjects in which Sir Peter's influence has been notable, and is dedicated to his 75th birthday. The opening section reviews some of his many remarkable contributions to mathematics and other fields. The remaining contributions come from leading researchers in analytic and arithmetic number theory, and algebraic geometry. The topics treated include: rational points on algebraic varieties, the Hasse principle, Shafarevich-Tate groups of elliptic curves and motives, Zagier's conjectures, descent and zero-cycles, Diophantine approximation, and Abelian and Fano varieties.

Introduction To String Theory

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Author : Sergio Cecotti
language : en
Publisher: Springer Nature
Release Date : 2023-10-06

Introduction To String Theory written by Sergio Cecotti and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-10-06 with Science categories.

Graduate students typically enter into courses on string theory having little to no familiarity with the mathematical background so crucial to the discipline. As such, this book, based on lecture notes, edited and expanded, from the graduate course taught by the author at SISSA and BIMSA, places particular emphasis on said mathematical background. The target audience for the book includes students of both theoretical physics and mathematics. This explains the book’s "strange" style: on the one hand, it is highly didactic and explicit, with a host of examples for the physicists, but, in addition, there are also almost 100 separate technical boxes, appendices, and starred sections, in which matters discussed in the main text are put into a broader mathematical perspective, while deeper and more rigorous points of view (particularly those from the modern era) are presented. The boxes also serve to further shore up the reader’s understanding of the underlying math. In writing this book, the author’s goal was not to achieve any sort of definitive conciseness, opting instead for clarity and "completeness". To this end, several arguments are presented more than once from different viewpoints and in varying contexts.

Lmsst 24 Lectures On Elliptic Curves

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Author : J. W. S. Cassels
language : en
Publisher: Cambridge University Press
Release Date : 1991-11-21

Lmsst 24 Lectures On Elliptic Curves written by J. W. S. Cassels 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 1991-11-21 with Mathematics categories.

The study of special cases of elliptic curves goes back to Diophantos and Fermat, and today it is still one of the liveliest centers of research in number theory. This book, addressed to beginning graduate students, introduces basic theory from a contemporary viewpoint but with an eye to the historical background. The central portion deals with curves over the rationals: the Mordell-Wei finite basis theorem, points of finite order (Nagell-Lutz), etc. The treatment is structured by the local-global standpoint and culminates in the description of the Tate-Shafarevich group as the obstruction to a Hasse principle. In an introductory section the Hasse principle for conics is discussed. The book closes with sections on the theory over finite fields (the "Riemann hypothesis for function fields") and recently developed uses of elliptic curves for factoring large integers. Prerequisites are kept to a minimum; an acquaintance with the fundamentals of Galois theory is assumed, but no knowledge either of algebraic number theory or algebraic geometry is needed. The p-adic numbers are introduced from scratch. Many examples and exercises are included for the reader, and those new to elliptic curves, whether they are graduate students or specialists from other fields, will find this a valuable introduction.

Geometric Modular Forms And Elliptic Curves

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Author : Haruzo Hida
language : en
Publisher: World Scientific
Release Date : 2000-09-27

Geometric Modular Forms And Elliptic Curves written by Haruzo Hida and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-09-27 with Mathematics categories.

This book provides a comprehensive account of the theory of moduli spaces of elliptic curves (over integer rings) and its application to modular forms. The construction of Galois representations, which play a fundamental role in Wiles' proof of the Shimura-Taniyama conjecture, is given. In addition, the book presents an outline of the proof of diverse modularity results of two-dimensional Galois representations (including that of Wiles), as well as some of the author's new results in that direction.

Lmsst 24 Lectures On Elliptic Curves

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Author : John William Scott Cassels
language : en
Publisher:
Release Date : 2014-05-14

Lmsst 24 Lectures On Elliptic Curves written by John William Scott Cassels and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-05-14 with MATHEMATICS categories.

A self-contained introductory text for beginning graduate students that is contemporary in approach without ignoring historical matters.

Cohomology Of Drinfeld Modular Varieties Part 1 Geometry Counting Of Points And Local Harmonic Analysis

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Author : Gérard Laumon
language : en
Publisher: Cambridge University Press
Release Date : 1996

Cohomology Of Drinfeld Modular Varieties Part 1 Geometry Counting Of Points And Local Harmonic Analysis written by Gérard Laumon 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 1996 with Mathematics categories.

Originally published in 1995, Cohomology of Drinfeld Modular Varieties aimed to provide an introduction, in two volumes, both to this subject and to the Langlands correspondence for function fields. These varieties are the analogues for function fields of the Shimura varieties over number fields. The Langlands correspondence is a conjectured link between automorphic forms and Galois representations over a global field. By analogy with the number-theoretic case, one expects to establish the conjecture for function fields by studying the cohomology of Drinfeld modular varieties, which has been done by Drinfeld himself for the rank two case. The present volume is devoted to the geometry of these varieties, and to the local harmonic analysis needed to compute their cohomology. Though the author considers only the simpler case of function rather than number fields, many important features of the number field case can be illustrated.

High Primes And Misdemeanours

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Author : Hugh C. Williams
language : en
Publisher: American Mathematical Soc.
Release Date :

High Primes And Misdemeanours written by Hugh C. Williams 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 Science categories.

This volume consists of a selection of papers based on presentations made at the international conference on number theory held in honor of Hugh Williams' sixtieth birthday. The papers address topics in the areas of computational and explicit number theory and its applications. The material is suitable for graduate students and researchers interested in number theory.

Modular Forms And Galois Cohomology

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Author : Haruzo Hida
language : en
Publisher: Cambridge University Press
Release Date : 2000-06-29

Modular Forms And Galois Cohomology written by Haruzo Hida 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 2000-06-29 with Mathematics categories.

Comprehensive account of recent developments in arithmetic theory of modular forms, for graduates and researchers.

Hilbert Modular Forms And Iwasawa Theory

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Author : Haruzo Hida
language : en
Publisher: Clarendon Press
Release Date : 2006-06-15

Hilbert Modular Forms And Iwasawa Theory written by Haruzo Hida and has been published by Clarendon Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-06-15 with Mathematics categories.

The 1995 work of Wiles and Taylor-Wiles opened up a whole new technique in algebraic number theory and, a decade on, the waves caused by this incredibly important work are still being felt. This book, authored by a leading researcher, describes the striking applications that have been found for this technique. In the book, the deformation theoretic techniques of Wiles-Taylor are first generalized to Hilbert modular forms (following Fujiwara's treatment), and some applications found by the author are then discussed. With many exercises and open questions given, this text is ideal for researchers and graduate students entering this research area.