O Minimality And Diophantine Geometry

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O Minimality And Diophantine Geometry

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Author : G. O. Jones
language : en
Publisher: Cambridge University Press
Release Date : 2015-08-13

O Minimality And Diophantine Geometry written by G. O. Jones 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 2015-08-13 with Mathematics categories.

This book brings the researcher up to date with recent applications of mathematical logic to number theory.

Model Theory Algebra And Geometry

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Author : Deirdre Haskell
language : en
Publisher: Cambridge University Press
Release Date : 2000-07-03

Model Theory Algebra And Geometry written by Deirdre Haskell 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 2000-07-03 with Mathematics categories.

Leading experts survey the connections between model theory and semialgebraic, subanalytic, p-adic, rigid and diophantine geometry.

Lecture Notes On O Minimal Structures And Real Analytic Geometry

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Author : Springer
language : en
Publisher:
Release Date : 2012-09-01

Lecture Notes On O Minimal Structures And Real Analytic Geometry written by Springer and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-09-01 with categories.

Fundamentals Of Diophantine Geometry

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Author : S. Lang
language : en
Publisher: Springer Science & Business Media
Release Date : 1983-08-29

Fundamentals Of Diophantine Geometry written by S. 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 1983-08-29 with Mathematics categories.

Diophantine problems represent some of the strongest aesthetic attractions to algebraic geometry. They consist in giving criteria for the existence of solutions of algebraic equations in rings and fields, and eventually for the number of such solutions. The fundamental ring of interest is the ring of ordinary integers Z, and the fundamental field of interest is the field Q of rational numbers. One discovers rapidly that to have all the technical freedom needed in handling general problems, one must consider rings and fields of finite type over the integers and rationals. Furthermore, one is led to consider also finite fields, p-adic fields (including the real and complex numbers) as representing a localization of the problems under consideration. We shall deal with global problems, all of which will be of a qualitative nature. On the one hand we have curves defined over say the rational numbers. Ifthe curve is affine one may ask for its points in Z, and thanks to Siegel, one can classify all curves which have infinitely many integral points. This problem is treated in Chapter VII. One may ask also for those which have infinitely many rational points, and for this, there is only Mordell's conjecture that if the genus is :;;; 2, then there is only a finite number of rational points.

Number Theory Iii

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Author : Serge Lang
language : en
Publisher: Springer Science & Business Media
Release Date : 1997-04-14

Number Theory Iii 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 1997-04-14 with Mathematics categories.

In 1988 Shafarevich asked me to write a volume for the Encyclopaedia of Mathematical Sciences on Diophantine Geometry. I said yes, and here is the volume. By definition, diophantine problems concern the solutions of equations in integers, or rational numbers, or various generalizations, such as finitely generated rings over Z or finitely generated fields over Q. The word Geometry is tacked on to suggest geometric methods. This means that the present volume is not elementary. For a survey of some basic problems with a much more elementary approach, see [La 9Oc]. The field of diophantine geometry is now moving quite rapidly. Out standing conjectures ranging from decades back are being proved. I have tried to give the book some sort of coherence and permanence by em phasizing structural conjectures as much as results, so that one has a clear picture of the field. On the whole, I omit proofs, according to the boundary conditions of the encyclopedia. On some occasions I do give some ideas for the proofs when these are especially important. In any case, a lengthy bibliography refers to papers and books where proofs may be found. I have also followed Shafarevich's suggestion to give examples, and I have especially chosen these examples which show how some classical problems do or do not get solved by contemporary in sights. Fermat's last theorem occupies an intermediate position. Al though it is not proved, it is not an isolated problem any more.

Heights In Diophantine Geometry

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Author : Enrico Bombieri
language : en
Publisher: Cambridge University Press
Release Date : 2007-09-06

Heights In Diophantine Geometry written by Enrico Bombieri 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 2007-09-06 with Mathematics categories.

Diophantine geometry has been studied by number theorists for thousands of years, this monograph is a bridge between the classical theory and modern approach via arithmetic geometry. The treatment is largely self-contained, with proofs given in full detail. Many results appear here for the first time.

Arithmetic Geometry Of Logarithmic Pairs And Hyperbolicity Of Moduli Spaces

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Author : Marc-Hubert Nicole
language : en
Publisher: Springer Nature
Release Date : 2020-10-31

Arithmetic Geometry Of Logarithmic Pairs And Hyperbolicity Of Moduli Spaces written by Marc-Hubert Nicole and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-10-31 with Mathematics categories.

This textbook introduces exciting new developments and cutting-edge results on the theme of hyperbolicity. Written by leading experts in their respective fields, the chapters stem from mini-courses given alongside three workshops that took place in Montréal between 2018 and 2019. Each chapter is self-contained, including an overview of preliminaries for each respective topic. This approach captures the spirit of the original lectures, which prepared graduate students and those new to the field for the technical talks in the program. The four chapters turn the spotlight on the following pivotal themes: The basic notions of o-minimal geometry, which build to the proof of the Ax–Schanuel conjecture for variations of Hodge structures; A broad introduction to the theory of orbifold pairs and Campana's conjectures, with a special emphasis on the arithmetic perspective; A systematic presentation and comparison between different notions of hyperbolicity, as an introduction to the Lang–Vojta conjectures in the projective case; An exploration of hyperbolicity and the Lang–Vojta conjectures in the general case of quasi-projective varieties. Arithmetic Geometry of Logarithmic Pairs and Hyperbolicity of Moduli Spaces is an ideal resource for graduate students and researchers in number theory, complex algebraic geometry, and arithmetic geometry. A basic course in algebraic geometry is assumed, along with some familiarity with the vocabulary of algebraic number theory.

Algebraic Geometry

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Author : Richard Thomas
language : en
Publisher: American Mathematical Soc.
Release Date : 2018-06-01

Algebraic Geometry written by Richard Thomas 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 2018-06-01 with Geometry, Algebraic categories.

This is Part 2 of a two-volume set. Since Oscar Zariski organized a meeting in 1954, there has been a major algebraic geometry meeting every decade: Woods Hole (1964), Arcata (1974), Bowdoin (1985), Santa Cruz (1995), and Seattle (2005). The American Mathematical Society has supported these summer institutes for over 50 years. Their proceedings volumes have been extremely influential, summarizing the state of algebraic geometry at the time and pointing to future developments. The most recent Summer Institute in Algebraic Geometry was held July 2015 at the University of Utah in Salt Lake City, sponsored by the AMS with the collaboration of the Clay Mathematics Institute. This volume includes surveys growing out of plenary lectures and seminar talks during the meeting. Some present a broad overview of their topics, while others develop a distinctive perspective on an emerging topic. Topics span both complex algebraic geometry and arithmetic questions, specifically, analytic techniques, enumerative geometry, moduli theory, derived categories, birational geometry, tropical geometry, Diophantine questions, geometric representation theory, characteristic and -adic tools, etc. The resulting articles will be important references in these areas for years to come.

Proceedings Of The International Congress Of Mathematicians 2018 Icm 2018 In 4 Volumes

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Author : Sirakov Boyan
language : en
Publisher: World Scientific
Release Date : 2019-02-27

Proceedings Of The International Congress Of Mathematicians 2018 Icm 2018 In 4 Volumes written by Sirakov Boyan and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-02-27 with Mathematics categories.

The Proceedings of the ICM publishes the talks, by invited speakers, at the conference organized by the International Mathematical Union every 4 years. It covers several areas of Mathematics and it includes the Fields Medal and Nevanlinna, Gauss and Leelavati Prizes and the Chern Medal laudatios.

Model Theory In Algebra Analysis And Arithmetic

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Author : Lou van den Dries
language : en
Publisher: Springer
Release Date : 2014-09-20

Model Theory In Algebra Analysis And Arithmetic written by Lou van den Dries and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-09-20 with Mathematics categories.

Presenting recent developments and applications, the book focuses on four main topics in current model theory: 1) the model theory of valued fields; 2) undecidability in arithmetic; 3) NIP theories; and 4) the model theory of real and complex exponentiation. Young researchers in model theory will particularly benefit from the book, as will more senior researchers in other branches of mathematics.