About this product

Product Identifiers

PublisherAmerican Mathematical Society

ISBN-100821802674

ISBN-139780821802670

eBay Product ID (ePID)966372

Product Key Features

Number of Pages397 Pages

LanguageEnglish

Publication NameInvitation to Arithmetic Geometry

SubjectGeometry / Algebraic

Publication Year1996

TypeTextbook

Subject AreaMathematics

AuthorDino Lorenzini

SeriesGraduate Studies in Mathematics Ser.

FormatHardcover

Dimensions

Item Height0.6 in

Item Weight23.5 Oz

Item Length9.8 in

Item Width5.9 in

Additional Product Features

Intended AudienceCollege Audience

LCCN95-024459

Dewey Edition20

TitleLeadingAn

Series Volume Number9

IllustratedYes

Dewey Decimal512/.74

Table Of ContentAn invitation to arithmetic geometry (entire volume); Description of the chapters; Integral closure (Chapter I); Plane curves (Chapter II); Factorization of ideals (Chapter III); The discriminants (Chapter IV); The ideal class group (Chapter V); Projective curves (Chapter VI); Nonsingular complete curves (Chapter VII); Zeta-functions (Chapter VIII); The Riemann-Roch Theorem (Chapter IX); Frobenius morphisms and the Riemann hypothesis (Chapter X); Further topics (Chapter XI); Appendix (Chapter XII); Glossary of notation; Index; Bibliography.

SynopsisLorenzini brings out the deep analogies between number theory, commutative algebra, and algebraic geometry. An Invitation to Arithmetic Geometry is designed to emphasize the interconnection between the two fields of mathematics. It presents in a unified manner the basic tools and concepts of number theory and algebraic geometry. Containing many worked-out examples and suggested exercises, the book was written as a graduate textbook for introductory arithmetic geometry., Presents some of the basic tools and concepts in number theory, commutative algebra, and algebraic geometry. This book presents the deep analogies between them. It also stresses on the geometric viewpoint., This work brings out the deep analogies between number theory, commutative algebra and algebraic geometry. It has been designed to emphasize the interconnection between the two fields of mathematics, and presents in a unified manner the basic tools and concepts of number theory and algebraic geometry. Containing worked-out examples and suggested exercises, the work was written as a textbook for a year-long introduction to arithmetic geometry., 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.

LC Classification NumberQA242.5.L67 1996

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Graduate Studies in Mathematics Ser.: Invitation to Arithmetic Geometry by Dino Lorenzini (1996, Hardcover)

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