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Geometry and arithmetic

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Published .
Written in English


  • Geometry,
  • Arithmetic

Book details:

Edition Notes

StatementCarel Faber, Gavril Farkas, Robin de Jong, editors
SeriesEMS series of congress reports
LC ClassificationsQA440 .G465 2012
The Physical Object
Paginationvi, 376 pages
Number of Pages376
ID Numbers
Open LibraryOL27041038M
ISBN 103037191198
ISBN 109783037191194

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Algebra, Arithmetic, and Geometry: In Honor of Yu. I. Manin consists of invited expository and research articles on new developments arising from Manin’s outstanding contributions to mathematics. Contributors in the first volume include:   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 Everyone knows what a rational number is, a quotient of two integers. We call a point (x, y) in the plane a rational point if both of its coordinates are rational call a line a rational line if the equation of the line can be written with rational numbers, that is, if it has an equation   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 ://

  Corry Geometry/Arithmetic in Euclid, Book II - 2 - 2. Introduction Book II of Euclid’s Elements raises interesting historical questions concerning its intended aims and significance. The book has been accorded a rather singular role in the recent historiography of Greek mathematics, particularly in the context of the ~corry/publications/articles/pdf/ Click the book cover above to read the entire Introductory Geometry and Arithmetic course. Or click here to download the full, printable pdf. The Arts of Liberty Project is an ongoing educational initiative at the University of Dallas that educates students, teachers, and lifelong learners in the purpose and power of the liberal arts and   1. Arithmetical algebraic geometry. I. Darmon, Henri, – QAA 5—dc22 Copying and reprinting. Material in this book may be reproduced by any means for edu-cational and scientific purposes without fee or permission with the exception of reproduction   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 eld of rational numbers) and F p (the nite eld of p elements), and their nite ://~poonen//

Euler Systems and Arithmetic Geometry. This note explains the following topics: Galois Modules, Discrete Valuation Rings, The Galois Theory of Local Fields, Ramification Groups, Witt Vectors, Projective Limits of Groups of Units of Finite Fields, The Absolute Galois Group of a Local Field, Group Cohomology, Galois Cohomology, Abelian Varieties, Selmer Groups of Abelian Varieties, Kummer The book provides a broad view of these subjects at the level of calculus, without being a calculus book. Its roots are in arithmetic and geometry, the two opposite poles of mathematics, and the source of historic conceptual conflict. The resolution of this conflict, and its role in the development of mathematics, is one of the main stories in  › Books › Science & Math › Mathematics. 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 , and presented some of the most interesting new developments in arithmetic geometry. This book collects the lecture notes which were written up by the  › Mathematics › Number Theory and Discrete Mathematics.   Arithmetic Geometry can be defined as the part of Algebraic Geometry connected with the study of algebraic varieties over arbitrary rings, in particular over non-algebraically closed fields. It lies at the intersection between classical algebraic geometry and number ://