Serres Conjecture
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| Author | : T.Y. Lam |
| Publisher | : Springer |
| Total Pages | : 240 |
| Release | : 2006-11-15 |
| Genre | : Mathematics |
| ISBN | : 3540359265 |
From the Preface: "I felt it would be useful for graduate students to see a detailed account of the sequence of mathematical developments which was inspired by the Conjecture, and which ultimately led to its full solution.... I offered a course on Serre's Conjecture to a small group of graduate students in January, 1977 [at the University of California, Berkeley] one year after its solution by Quillen and Suslin. My course was taught very much in the spirit of a mathematical 'guided tour'. Volunteering as the guide, I took upon myself the task of charting a route through all the beautiful mathematics surrounding the main problem to be treated; the 'guide' then leads his audience through the route, on to the destination, pointing out the beautiful sceneries and historical landmarks along the way."
| Author | : T.Y. Lam |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 412 |
| Release | : 2010-05-17 |
| Genre | : Mathematics |
| ISBN | : 3540345752 |
An invaluable summary of research work done in the period from 1978 to the present
| Author | : Gary Cornell |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 608 |
| Release | : 1997 |
| Genre | : Mathematics |
| ISBN | : 9780387946092 |
A collection of expanded versions of lectures given at an instructional conference on number theory and arithmetic geometry held at Boston University. The purpose of the conference, and indeed this book, is to introduce and explain the many ideas and techniques used by Wiles in his proof, and to explain how his result can be combined with Ribet's theorem and ideas of Frey and Serre to show, at long last, that Fermat's Last Theorem is true. The book begins with an overview of the complete proof, theory of elliptic curves, modular functions, modular curves, Galois cohomology, and finite group schemes. In recognition of the historical significance of Fermat's Last Theorem, the volume concludes by reflecting on the history of the problem, while placing Wiles' theorem into a more general Diophantine context suggesting future applications.
| Author | : Mehmet Haluk Şengün |
| Publisher | : |
| Total Pages | : 104 |
| Release | : 2008 |
| Genre | : |
| ISBN | : |
| Author | : Vijaya Kumar Murty |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 278 |
| Release | : 1995 |
| Genre | : Mathematics |
| ISBN | : 0821803131 |
The most significant recent development in number theory is the work of Andrew Wiles on modular elliptic curves. Besides implying Fermat's Last Theorem, his work establishes a new reciprocity law. Reciprocity laws lie at the heart of number theory. Wiles' work draws on many of the tools of modern number theory and the purpose of this volume is to introduce readers to some of this background material. Based on a seminar held during 1993-1994 at the Fields Institute for Research in Mathematical Sciences, this book contains articles on elliptic curves, modular forms and modular curves, Serre's conjectures, Ribet's theorem, deformations of Galois representations, Euler systems, and annihilators of Selmer groups. All of the authors are well known in their field and have made significant contributions to the general area of elliptic curves, Galois representations, and modular forms. Features: Brings together a unique collection of number theoretic tools. Makes accessible the tools needed to understand one of the biggest breakthroughs in mathematics. Provides numerous references for further study.
| Author | : Brian David Conrad |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 588 |
| Release | : |
| Genre | : Mathematics |
| ISBN | : 9780821886915 |
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.
| Author | : Skip Garibaldi |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 344 |
| Release | : 2010-07-16 |
| Genre | : Mathematics |
| ISBN | : 1441962115 |
Developments in Mathematics is a book series devoted to all areas of mathematics, pure and applied. The series emphasizes research monographs describing the latest advances. Edited volumes that focus on areas that have seen dramatic progress, or are of special interest, are encouraged as well.
| Author | : Jean-P. Serre |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 228 |
| Release | : 2013-06-29 |
| Genre | : Technology & Engineering |
| ISBN | : 3663106322 |
The book is based on a course given by J.-P. Serre at the Collège de France in 1980 and 1981. Basic techniques in Diophantine geometry are covered, such as heights, the Mordell-Weil theorem, Siegel's and Baker's theorems, Hilbert's irreducibility theorem, and the large sieve. Included are applications to, for example, Mordell's conjecture, the construction of Galois extensions, and the classical class number 1 problem. Comprehensive bibliographical references.
| Author | : Peter Hilton |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 176 |
| Release | : 1985 |
| Genre | : Mathematics |
| ISBN | : 0821850369 |
This book, which is the proceedings of a conference held at Memorial University of Newfoundland, August 1983, contains 18 papers in algebraic topology and homological algebra by collaborators and associates of Peter Hilton. It is dedicated to Hilton on the occasion of his 60th birthday. The various topics covered are homotopy theory, $H$-spaces, group cohomology, localization, classifying spaces, and Eckmann-Hilton duality. Students and researchers in algebraic topology will gain an appreciation for Hilton's impact upon mathematics from reading this book.
| Author | : Hyman Bass |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 250 |
| Release | : 1999 |
| Genre | : Mathematics |
| ISBN | : 0821810871 |
This volume includes expositions of key developments over the past four decades in commutative and non-commutative algebra, algebraic $K$-theory, infinite group theory, and applications of algebra to topology. Many of the articles are based on lectures given at a conference at Columbia University honoring the 65th birthday of Hyman Bass. Important topics related to Bass's mathematical interests are surveyed by leading experts in the field. Of particular note is a professional autobiography of Professor Bass, and an article by Deborah Ball on mathematical education. The range of subjects covered in the book offers a convenient single source for topics in the field.
