Arithmetic Algebraic Geometry

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Arithmetic Algebraic Geometry

Brian David Conrad
Arithmetic Algebraic Geometry Book PDF

Author : Brian David Conrad
Publisher : American Mathematical Soc.
Page : 588 pages
File Size : 52,8 Mb
Release : 2024-06-26
Category : Mathematics
ISBN : 0821886916

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Arithmetic Algebraic Geometry by Brian David Conrad Pdf

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.

Algebraic Geometry and Arithmetic Curves

Qing Liu,Reinie Erne
Algebraic Geometry and Arithmetic Curves Book PDF

Author : Qing Liu,Reinie Erne
Publisher : Oxford University Press
Page : 593 pages
File Size : 50,7 Mb
Release : 2006-06-29
Category : Mathematics
ISBN : 9780191547805

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Algebraic Geometry and Arithmetic Curves by Qing Liu,Reinie Erne Pdf

This book is a general introduction to the theory of schemes, followed by applications to arithmetic surfaces and to the theory of reduction of algebraic curves. The first part introduces basic objects such as schemes, morphisms, base change, local properties (normality, regularity, Zariski's Main Theorem). This is followed by the more global aspect: coherent sheaves and a finiteness theorem for their cohomology groups. Then follows a chapter on sheaves of differentials, dualizing sheaves, and Grothendieck's duality theory. The first part ends with the theorem of Riemann-Roch and its application to the study of smooth projective curves over a field. Singular curves are treated through a detailed study of the Picard group. The second part starts with blowing-ups and desingularisation (embedded or not) of fibered surfaces over a Dedekind ring that leads on to intersection theory on arithmetic surfaces. Castelnuovo's criterion is proved and also the existence of the minimal regular model. This leads to the study of reduction of algebraic curves. The case of elliptic curves is studied in detail. The book concludes with the funadmental theorem of stable reduction of Deligne-Mumford. The book is essentially self-contained, including the necessary material on commutative algebra. The prerequisites are therefore few, and the book should suit a graduate student. It contains many examples and nearly 600 exercises.

Galois Representations in Arithmetic Algebraic Geometry

A. J. Scholl,Richard Lawrence Taylor
Galois Representations in Arithmetic Algebraic Geometry Book PDF

Author : A. J. Scholl,Richard Lawrence Taylor
Publisher : Cambridge University Press
Page : 506 pages
File Size : 53,7 Mb
Release : 1998-11-26
Category : Mathematics
ISBN : 9780521644198

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Galois Representations in Arithmetic Algebraic Geometry by A. J. Scholl,Richard Lawrence Taylor Pdf

Conference proceedings based on the 1996 LMS Durham Symposium 'Galois representations in arithmetic algebraic geometry'.

Arithmetic Algebraic Geometry

G., van der Geer,F. Oort,J.H.M. Steenbrink
Arithmetic Algebraic Geometry Book PDF

Author : G., van der Geer,F. Oort,J.H.M. Steenbrink
Publisher : Springer Science & Business Media
Page : 450 pages
File Size : 51,9 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461204572

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Arithmetic Algebraic Geometry by G., van der Geer,F. Oort,J.H.M. Steenbrink Pdf

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. 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.

Algebra, Arithmetic, and Geometry

Yuri Tschinkel,Yuri Zarhin
Algebra Arithmetic and Geometry Book PDF

Author : Yuri Tschinkel,Yuri Zarhin
Publisher : Springer Science & Business Media
Page : 700 pages
File Size : 55,5 Mb
Release : 2010-04-11
Category : Mathematics
ISBN : 9780817647476

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Algebra, Arithmetic, and Geometry by Yuri Tschinkel,Yuri Zarhin Pdf

EMAlgebra, Arithmetic, and Geometry: In Honor of Yu. I. ManinEM consists of invited expository and research articles on new developments arising from Manin’s outstanding contributions to mathematics.

An Invitation to Arithmetic Geometry

Dino Lorenzini
An Invitation to Arithmetic Geometry Book PDF

Author : Dino Lorenzini
Publisher : American Mathematical Society
Page : 397 pages
File Size : 55,7 Mb
Release : 2021-12-23
Category : Mathematics
ISBN : 9781470467258

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An Invitation to Arithmetic Geometry by Dino Lorenzini Pdf

Extremely carefully written, masterfully thought out, and skillfully arranged introduction … to the arithmetic of algebraic curves, on the one hand, and to the algebro-geometric aspects of number theory, on the other hand. … an excellent guide for beginners in arithmetic geometry, just as an interesting reference and methodical inspiration for teachers of the subject … a highly welcome addition to the existing literature. —Zentralblatt MATH The interaction between number theory and algebraic geometry has been especially fruitful. In this volume, the author gives a unified presentation of some of the basic tools and concepts in number theory, commutative algebra, and algebraic geometry, and for the first time in a book at this level, brings out the deep analogies between them. The geometric viewpoint is stressed throughout the book. Extensive examples are given to illustrate each new concept, and many interesting exercises are given at the end of each chapter. Most of the important results in the one-dimensional case are proved, including Bombieri's proof of the Riemann Hypothesis for curves over a finite field. While the book is not intended to be an introduction to schemes, the author indicates how many of the geometric notions introduced in the book relate to schemes, which will aid the reader who goes to the next level of this rich subject.

Arithmetic Algebraic Geometry

Jean-Louis Colliot-Thelene,Kazuya Kato,Paul Vojta
Arithmetic Algebraic Geometry Book PDF

Author : Jean-Louis Colliot-Thelene,Kazuya Kato,Paul Vojta
Publisher : Springer
Page : 218 pages
File Size : 46,8 Mb
Release : 2006-11-15
Category : Mathematics
ISBN : 9783540479093

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Arithmetic Algebraic Geometry by Jean-Louis Colliot-Thelene,Kazuya Kato,Paul Vojta Pdf

This volume contains three long lecture series by J.L. Colliot-Thelene, Kazuya Kato and P. Vojta. Their topics are respectively the connection between algebraic K-theory and the torsion algebraic cycles on an algebraic variety, a new approach to Iwasawa theory for Hasse-Weil L-function, and the applications of arithemetic geometry to Diophantine approximation. They contain many new results at a very advanced level, but also surveys of the state of the art on the subject with complete, detailed profs and a lot of background. Hence they can be useful to readers with very different background and experience. CONTENTS: J.L. Colliot-Thelene: Cycles algebriques de torsion et K-theorie algebrique.- K. Kato: Lectures on the approach to Iwasawa theory for Hasse-Weil L-functions.- P. Vojta: Applications of arithmetic algebraic geometry to diophantine approximations.

Arithmetic of Higher-Dimensional Algebraic Varieties

Bjorn Poonen,Yuri Tschinkel
Arithmetic of Higher Dimensional Algebraic Varieties Book PDF

Author : Bjorn Poonen,Yuri Tschinkel
Publisher : Springer Science & Business Media
Page : 292 pages
File Size : 51,9 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9780817681708

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Arithmetic of Higher-Dimensional Algebraic Varieties by Bjorn Poonen,Yuri Tschinkel Pdf

This text offers a collection of survey and research papers by leading specialists in the field documenting the current understanding of higher dimensional varieties. Recently, it has become clear that ideas from many branches of mathematics can be successfully employed in the study of rational and integral points. This book will be very valuable for researchers from these various fields who have an interest in arithmetic applications, specialists in arithmetic geometry itself, and graduate students wishing to pursue research in this area.

Conjectures in Arithmetic Algebraic Geometry

Wilfred W. J. Hulsbergen
Conjectures in Arithmetic Algebraic Geometry Book PDF

Author : Wilfred W. J. Hulsbergen
Publisher : Springer Science & Business Media
Page : 246 pages
File Size : 52,8 Mb
Release : 2013-06-29
Category : Technology & Engineering
ISBN : 9783663095057

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Conjectures in Arithmetic Algebraic Geometry by Wilfred W. J. Hulsbergen Pdf

In the early 1980's, stimulated by work of Bloch and Deligne, Beilinson stated some intriguing conjectures on special values of L-functions of algebraic varieties defined over number fields. Roughly speaking these special values are determinants of higher regulator maps relating the higher algebraic K-groups of the variety to its cohomology. In this respect, higher algebraic K-theory is believed to provide a universal, motivic cohomology theory and the regulator maps are determined by Chern characters from higher algebraic K-theory to any other suitable cohomology theory. Also, Beilinson stated a generalized Hodge conjecture. This book provides an introduction to and a survey of Beilinson's conjectures and an introduction to Jannsen's work with respect to the Hodge and Tate conjectures. It addresses mathematicians with some knowledge of algebraic number theory, elliptic curves and algebraic K-theory.

Algebraic Geometry

Daniel Perrin
Algebraic Geometry Book PDF

Author : Daniel Perrin
Publisher : Springer Science & Business Media
Page : 267 pages
File Size : 53,8 Mb
Release : 2007-12-16
Category : Mathematics
ISBN : 9781848000568

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Algebraic Geometry by Daniel Perrin Pdf

Aimed primarily at graduate students and beginning researchers, this book provides an introduction to algebraic geometry that is particularly suitable for those with no previous contact with the subject; it assumes only the standard background of undergraduate algebra. The book starts with easily-formulated problems with non-trivial solutions and uses these problems to introduce the fundamental tools of modern algebraic geometry: dimension; singularities; sheaves; varieties; and cohomology. A range of exercises is provided for each topic discussed, and a selection of problems and exam papers are collected in an appendix to provide material for further study.

Introduction to Algebraic Geometry

Serge Lang
Introduction to Algebraic Geometry Book PDF

Author : Serge Lang
Publisher : Courier Dover Publications
Page : 273 pages
File Size : 55,5 Mb
Release : 2019-03-20
Category : Mathematics
ISBN : 9780486839806

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Introduction to Algebraic Geometry by Serge Lang Pdf

Author Serge Lang defines algebraic geometry as the study of systems of algebraic equations in several variables and of the structure that one can give to the solutions of such equations. The study can be carried out in four ways: analytical, topological, algebraico-geometric, and arithmetic. This volume offers a rapid, concise, and self-contained introductory approach to the algebraic aspects of the third method, the algebraico-geometric. The treatment assumes only familiarity with elementary algebra up to the level of Galois theory. Starting with an opening chapter on the general theory of places, the author advances to examinations of algebraic varieties, the absolute theory of varieties, and products, projections, and correspondences. Subsequent chapters explore normal varieties, divisors and linear systems, differential forms, the theory of simple points, and algebraic groups, concluding with a focus on the Riemann-Roch theorem. All the theorems of a general nature related to the foundations of the theory of algebraic groups are featured.

An Invitation to Arithmetic Geometry

Dino Lorenzini
An Invitation to Arithmetic Geometry Book PDF

Author : Dino Lorenzini
Publisher : American Mathematical Soc.
Page : 418 pages
File Size : 50,6 Mb
Release : 1996-02-22
Category : Arithmetical algebraic geometry
ISBN : 9780821802670

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An Invitation to Arithmetic Geometry by Dino Lorenzini Pdf

Extremely carefully written, masterfully thought out, and skillfully arranged introduction ... to the arithmetic of algebraic curves, on the one hand, and to the algebro-geometric aspects of number theory, on the other hand. ... an excellent guide for beginners in arithmetic geometry, just as an interesting reference and methodical inspiration for teachers of the subject ... a highly welcome addition to the existing literature. --Zentralblatt MATH The interaction between number theory and algebraic geometry has been especially fruitful. In this volume, the author gives a unified presentation of some of the basic tools and concepts in number theory, commutative algebra, and algebraic geometry, and for the first time in a book at this level, brings out the deep analogies between them. The geometric viewpoint is stressed throughout the book. Extensive examples are given to illustrate each new concept, and many interesting exercises are given at the end of each chapter. Most of the important results in the one-dimensional case are proved, including Bombieri's proof of the Riemann Hypothesis for curves over a finite field. While the book is not intended to be an introduction to schemes, the author indicates how many of the geometric notions introduced in the book relate to schemes, which will aid the reader who goes to the next level of this rich subject.

Arithmetic of Algebraic Curves

Serguei A. Stepanov
Arithmetic of Algebraic Curves Book PDF

Author : Serguei A. Stepanov
Publisher : Springer Science & Business Media
Page : 444 pages
File Size : 48,6 Mb
Release : 1994-12-31
Category : Mathematics
ISBN : 0306110369

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Arithmetic of Algebraic Curves by Serguei A. Stepanov Pdf

Author S.A. Stepanov thoroughly investigates the current state of the theory of Diophantine equations and its related methods. Discussions focus on arithmetic, algebraic-geometric, and logical aspects of the problem. Designed for students as well as researchers, the book includes over 250 excercises accompanied by hints, instructions, and references. Written in a clear manner, this text does not require readers to have special knowledge of modern methods of algebraic geometry.

Arithmetic Geometry

G. Cornell,J. H. Silverman
Arithmetic Geometry Book PDF

Author : G. Cornell,J. H. Silverman
Publisher : Springer Science & Business Media
Page : 359 pages
File Size : 53,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461386551

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Arithmetic Geometry by G. Cornell,J. H. Silverman Pdf

This volume is the result of a (mainly) instructional conference on arithmetic geometry, held from July 30 through August 10, 1984 at the University of Connecticut in Storrs. This volume contains expanded versions of almost all the instructional lectures given during the conference. In addition to these expository lectures, this volume contains a translation into English of Falt ings' seminal paper which provided the inspiration for the conference. We thank Professor Faltings for his permission to publish the translation and Edward Shipz who did the translation. We thank all the people who spoke at the Storrs conference, both for helping to make it a successful meeting and enabling us to publish this volume. We would especially like to thank David Rohrlich, who delivered the lectures on height functions (Chapter VI) when the second editor was unavoidably detained. In addition to the editors, Michael Artin and John Tate served on the organizing committee for the conference and much of the success of the conference was due to them-our thanks go to them for their assistance. Finally, the conference was only made possible through generous grants from the Vaughn Foundation and the National Science Foundation.

Algebraic Geometry and Arithmetic Curves

刘擎,Centre National de La Recherche Scientifique (Cnrs) Laboratoire de Theorie Des Nombres Et D'Algorithmique Arithmetique Qing Liu
Algebraic Geometry and Arithmetic Curves Book PDF

Author : 刘擎,Centre National de La Recherche Scientifique (Cnrs) Laboratoire de Theorie Des Nombres Et D'Algorithmique Arithmetique Qing Liu
Publisher : Oxford University Press on Demand
Page : 594 pages
File Size : 42,8 Mb
Release : 2002
Category : Mathematics
ISBN : 9780198502845

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Algebraic Geometry and Arithmetic Curves by 刘擎,Centre National de La Recherche Scientifique (Cnrs) Laboratoire de Theorie Des Nombres Et D'Algorithmique Arithmetique Qing Liu Pdf

This new-in-paperback edition provides an introduction to algebraic and arithmetic geometry, starting with the theory of schemes, followed by applications to arithmetic surfaces and to the theory of reduction of algebraic curves. Clear explanations of both theory and applications, and almost 600 exercises are included in the text. - ;This new-in-paperback edition provides a general introduction to algebraic and arithmetic geometry, starting with the theory of schemes, followed by applications to arithmetic surfaces and to the theory of reduction of algebraic curves. The first part introduces b.