Arithmetic geometry

Cover of: Arithmetic geometry |

Published by American Mathematical Society, Clay Mathematics Institute in Providence, RI, [Cambridge, MA] .

Written in English

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Subjects:

  • Arithmetical algebraic geometry

Edition Notes

Includes bibliographical references.

Book details

StatementHenri Darmon ... [et al.], editors.
SeriesClay mathematics proceedings -- v. 8
ContributionsDarmon, Henri, 1965-
Classifications
LC ClassificationsQA242.5 .A754 2009
The Physical Object
Paginationp. cm.
ID Numbers
Open LibraryOL23622016M
ISBN 109780821844762
LC Control Number2009027374
OCLC/WorldCa426147200

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out of 5 stars /5(2). A Generalized Arithmetic Geometric Mean. This note explains the following topics: Classical arithmetic geometry, The Convergence Theorem, The link with the classical AGM sequence, Point counting on elliptic curves, A theta structure induced by Frobenius.

Advice for potential graduate students in Arithmetic Geometry. "The geometry of schemes" and Eisenbud's commutative algebra book, as well as William Stein's latex'd notes from Hartshorne's algebraic geometry course.) There of course is a small bit of healthy disagreement.

If I were writing the syllabus for an AG qual, the above would. Arithmetic geometry is the same except that one is interested instead in the solutions where the coordinates lie in other elds that are usually far from being algebraically closed.

Fields of special interest are Q (the Arithmetic geometry book of rational numbers) and F p (the nite eld of p elements), and their nite Size: KB. This book presents an introductory account of the subject in the style of the original discoverers, with references to and comments about more recent and modern developments.

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edit: For moduli of elliptic curves, Chapter 1 (Modular forms) of "Advanced topics" is a good place to start, and Katz-Mazur is a good eventual target. Arithmetic and Geometry presents highlights of recent work in arithmetic algebraic geometry by some of the world’s leading mathematicians.

Together, these lectures—which were delivered in celebration of the tenth anniversary of the annual summer workshops in Alpbach, Austria—provide an introduction to high-level research on three topics: Shimura varieties, hyperelliptic continued.

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 Septemberand presented some of the most interesting new developments in arithmetic geometry.

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Serre, Jean-Pierre. A Course in Arithmetic. Springer-Verlag,   The School provided a unique opportunity to introduce graduate students to analytic methods in arithmetic geometry. The book contains four articles. Alina C.

Cojocaru's article introduces sieving techniques to study the group structure of points of the reduction of an elliptic curve modulo a rational prime via its division fields.

This volume is the result of a (mainly) instructional conference on arithmetic geometry, held from July 30 through Aug at the University of Connecticut in Storrs. This volume contains expanded versions of almost all the instructional lectures given during the conference.

This book is intended to give a serious and reasonably complete introduction to algebraic geometry, not just for (future) experts in the field. The exposition serves a narrow set of goals (see §), and necessarily takes a particular point of view on the subject.

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[Álvaro Lozano-Robledo] -- Geometry and the theory of numbers are as old as some of the oldest historical records of humanity. Ever since antiquity, mathematicians have discovered many beautiful interactions between the two.

A Master of Numbers and Shapes Who Is Rewriting Arithmetic. By Erica Klarreich. August 1, Read Later. The year-old math sensation Peter Scholze is now one of the youngest Fields medalists for “the revolution that he launched in arithmetic geometry.”.

euclidean geometry may be developed without the use of the axiom of continuity; the signifi-cance of Desargues’s theorem, as a condition that a given plane geometry may be regarded as a part of a geometry of space, is made apparent, etc.

A variety of algebras of segments are introduced in accordance with the laws of arithmetic. Nancy Childress, John W. Jones (editors), Arithmetic Geometry: Conference on Arithmetic Geometry with an Emphasis on Iwasawa Theory, American Mathematical Society, back cover, This book resulted from a research conference in arithmetic geometry held at.

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Diophantine geometry of Abelian and Shimura varieties [24, 36]. On the other hand an arithmetic di erential geometry was developed in a series of papers [42]-[47], [8]; the present book follows, and further develops, the theory in this latter series of papers. We should note that our book [35] on arithmetic di erential equations and.

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