Higher Dimensional Geometry Over Finite Fields

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Higher Dimensional Geometry Over Finite Fields

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Author : Dmitri Kaledin
language : en
Publisher: IOS Press
Release Date : 2008

Higher Dimensional Geometry Over Finite Fields written by Dmitri Kaledin and has been published by IOS Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Mathematics categories.

"Proceedings of the NATO Advanced Study Institute on Higher-Dimensional Geometry over Finite Fields, Geottingen, Germany, 25 June-6 July 2007."--T.p. verso.

Higher Dimensional Geometry Over Finite Fields

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Author : D. Kaledin
language : en
Publisher:
Release Date : 2008

Higher Dimensional Geometry Over Finite Fields written by D. Kaledin and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Finite fields (Algebra) categories.

Number systems based on a finite collection of symbols, such as the 0s and 1s of computer circuitry, are ubiquitous in the modern age. Finite fields are the important number systems. This title introduces the reader to the developments in algebraic geometry over finite fields.

Handbook Of Finite Fields

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Author : Gary L. Mullen
language : en
Publisher: CRC Press
Release Date : 2013-06-17

Handbook Of Finite Fields written by Gary L. Mullen and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-06-17 with Computers categories.

Poised to become the leading reference in the field, the Handbook of Finite Fields is exclusively devoted to the theory and applications of finite fields. More than 80 international contributors compile state-of-the-art research in this definitive handbook. Edited by two renowned researchers, the book uses a uniform style and format throughout and

Arithmetic Geometry

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Author : Jean-Louis Colliot-Thélène
language : en
Publisher: Springer
Release Date : 2010-10-27

Arithmetic Geometry written by Jean-Louis Colliot-Thélène and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-10-27 with Mathematics categories.

Arithmetic Geometry can be defined as the part of Algebraic Geometry connected with the study of algebraic varieties through arbitrary rings, in particular through non-algebraically closed fields. It lies at the intersection between classical algebraic geometry and number theory. A C.I.M.E. Summer School devoted to arithmetic geometry was held in Cetraro, Italy in September 2007, and presented some of the most interesting new developments in arithmetic geometry. This book collects the lecture notes which were written up by the speakers. The main topics concern diophantine equations, local-global principles, diophantine approximation and its relations to Nevanlinna theory, and rationally connected varieties. The book is divided into three parts, corresponding to the courses given by J-L Colliot-Thelene, Peter Swinnerton Dyer and Paul Vojta.

Complex Multiplication And Lifting Problems

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Author : Ching-Li Chai
language : en
Publisher: American Mathematical Soc.
Release Date : 2013-12-19

Complex Multiplication And Lifting Problems written by Ching-Li Chai 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 2013-12-19 with Mathematics categories.

Abelian varieties with complex multiplication lie at the origins of class field theory, and they play a central role in the contemporary theory of Shimura varieties. They are special in characteristic 0 and ubiquitous over finite fields. This book explores the relationship between such abelian varieties over finite fields and over arithmetically interesting fields of characteristic 0 via the study of several natural CM lifting problems which had previously been solved only in special cases. In addition to giving complete solutions to such questions, the authors provide numerous examples to illustrate the general theory and present a detailed treatment of many fundamental results and concepts in the arithmetic of abelian varieties, such as the Main Theorem of Complex Multiplication and its generalizations, the finer aspects of Tate's work on abelian varieties over finite fields, and deformation theory. This book provides an ideal illustration of how modern techniques in arithmetic geometry (such as descent theory, crystalline methods, and group schemes) can be fruitfully combined with class field theory to answer concrete questions about abelian varieties. It will be a useful reference for researchers and advanced graduate students at the interface of number theory and algebraic geometry.

Arithmetic Of L Functions

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Author : Cristian Popescu
language : en
Publisher: American Mathematical Soc.
Release Date :

Arithmetic Of L Functions written by Cristian Popescu 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.

Mathematical Research Today And Tomorrow

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Author : Carlos Casacuberta
language : en
Publisher: Springer Science & Business Media
Release Date : 1992-12-14

Mathematical Research Today And Tomorrow written by Carlos Casacuberta 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 1992-12-14 with Mathematics categories.

The Symposium on the Current State and Prospects of Mathematics was held in Barcelona from June 13 to June 18, 1991. Seven invited Fields medalists gavetalks on the development of their respective research fields. The contents of all lectures were collected in the volume, together witha transcription of a round table discussion held during the Symposium. All papers are expository. Some parts include precise technical statements of recent results, but the greater part consists of narrative text addressed to a very broad mathematical public. CONTENTS: R. Thom: Leaving Mathematics for Philosophy.- S. Novikov: Role of Integrable Models in the Development of Mathematics.- S.-T. Yau: The Current State and Prospects of Geometry and Nonlinear Differential Equations.- A. Connes: Noncommutative Geometry.- S. Smale: Theory of Computation.- V. Jones: Knots in Mathematics and Physics.- G. Faltings: Recent Progress in Diophantine Geometry.

Enriques Surfaces Ii

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Author : Igor Dolgachev
language : en
Publisher: Springer Nature
Release Date : 2025-03-25

Enriques Surfaces Ii written by Igor Dolgachev and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-03-25 with Mathematics categories.

This book, consisting of two volumes, gives a contemporary account of the study of the class of projective algebraic surfaces known as Enriques surfaces. These surfaces were discovered more than 125 years by F. Enriques in an attempt to extend the characterization of rational algebraic curves to the case of algebraic surfaces. The novel feature of the present exposition is that no assumption on the characteristic of the ground field is assumed. This requirement calls for exploring the geometry of such surfaces by purely geometric and arithmetic methods that do not rely on transcendental methods such as the theory of periods of algebraic surfaces of type K3, which are close relatives of Enriques surfaces. Some of the methods use many technical tools from algebraic geometry that are discussed in Volume 1 and will be a useful source of reference for the study of algebraic surfaces over fields of positive characteristic. Volume 1 also contains a detailed exposition of the theory of elliptic surfaces over fields of arbitrary characteristic. The second volume discusses many new topics — for example, the theory of automorphisms of Enriques surfaces and the relationships with hyperbolic geometry. Together, the two volumes contain many examples and an extensive bibliography made up of more than 700 items.

Collected Papers Iv

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Author : Serge Lang
language : en
Publisher: Springer Science & Business Media
Release Date : 2000-07-28

Collected Papers Iv written by Serge Lang 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 2000-07-28 with Mathematics categories.

Serge Lang is not only one of the top mathematicians of our time, but also an excellent writer. He has made innumerable and invaluable contributions in diverse fields of mathematics and was honoured with the Cole Prize by the American Mathematical Society as well as with the Prix Carriere by the French Academy of Sciences. Here, 83 of his research papers are collected in four volumes, ranging over a variety of topics of interest to many readers.

Cubic Forms And The Circle Method

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Author : Tim Browning
language : en
Publisher: Springer Nature
Release Date : 2021-11-19

Cubic Forms And The Circle Method written by Tim Browning and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-11-19 with Mathematics categories.

The Hardy–Littlewood circle method was invented over a century ago to study integer solutions to special Diophantine equations, but it has since proven to be one of the most successful all-purpose tools available to number theorists. Not only is it capable of handling remarkably general systems of polynomial equations defined over arbitrary global fields, but it can also shed light on the space of rational curves that lie on algebraic varieties. This book, in which the arithmetic of cubic polynomials takes centre stage, is aimed at bringing beginning graduate students into contact with some of the many facets of the circle method, both classical and modern. This monograph is the winner of the 2021 Ferran Sunyer i Balaguer Prize, a prestigious award for books of expository nature presenting the latest developments in an active area of research in mathematics.