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25 Remote Warehouse Mathematics- Algebraic Geometry

This title in other editions

Arithmetic of Higher-dimensional Algebraic Varieties

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Arithmetic of Higher-dimensional Algebraic Varieties Cover

 

Synopses & Reviews

Publisher Comments:

One of the great successes of twentieth century mathematics has been the remarkable qualitative understanding of rational and integral points on curves, gleaned in part through the theorems of Mordell, Weil, Siegel, and Faltings. It has become clear that the study of rational and integral points has deep connections to other branches of mathematics: complex algebraic geometry, Galois and étale cohomology, transcendence theory and diophantine approximation, harmonic analysis, automorphic forms, and analytic number theory.   This text, which focuses on higher-dimensional varieties, provides precisely such an interdisciplinary view of the subject. It is a digest of research and survey papers by leading specialists; the book documents current knowledge in higher-dimensional arithmetic and gives indications for future research. It will be valuable not only to practitioners in the field, but to a wide audience of mathematicians and graduate students with an interest in arithmetic geometry.   Contributors: Batyrev, V.V.; Broberg, N.; Colliot-Thélène, J-L.; Ellenberg, J.S.; Gille, P.; Graber, T.; Harari, D.; Harris, J.; Hassett, B.; Heath-Brown, R.; Mazur, B.; Peyre, E.; Poonen, B.; Popov, O.N.; Raskind, W.; Salberger, P.; Scharaschkin, V.; Shalika, J.; Starr, J.; Swinnerton-Dyer, P.; Takloo-Bighash, R.; Tschinkel, Y.: Voloch, J.F.; Wittenberg, O.

Synopsis:

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.

Table of Contents

Abstracts.- Introduction.- Part I. Expository Articles. Swinnerton-Dyer, P.: Diophantine equations: progress and problems. Heath-Brown, R.: Rational points and analytic number theory. Harari, D.: Weak approximation on algebraic varieties. Peyre, E.: Counting points on varieties using universal torsors.- Part II. Research Articles. Batyrev, V.V.; Popov, O.N.: The Cox ring of a Del Pezzo surface. Broberg, N.; Salberger, P.: Counting rational points on threefolds. Colliot-Thélène, J-L.; Gille, P.: Remarques sur l'approximation faible sur un corps de fonctions d'une variable. Ellenberg, J.S.: K3 surfaces over number fields with geometric Picard number one. Graber, T.; Harris, J.; Mazur, B.; Starr, J.: Jumps in Mordell-Weil rank and Arithmetic Surjectivity. Hassett, B.; Tschinkel, Y.: Universal torsors and Cox rings. Poonen, B.; Voloch, J.F.: Random diophantine equations. Raskind, W.; Scharaschkin, V.: Descent on simply connected surfaces over algebraic number fields. Shalika, J.; Takloo-Bighash, R.; Tschinkel, Y.: Rational points on compactification of semi-simple groups of rank 1. Swinnerton-Dyer, P.: Weak Approximation on Del Pezzo surfaces of degree 4. Whittenberg, O.: Transcendental Brauer-Manin obstruction on a pencil of elliptic curves. - Glossary - Index

Product Details

ISBN:
9780817632595
Author:
Poonen, Bjorn
Publisher:
Birkhauser
Editor:
Tschinkel, Yuri
Author:
Tschinkel, Yuri
Subject:
Number Theory
Subject:
Algebra - Abstract
Subject:
Geometry - Algebraic
Subject:
Algebraic Geometry
Subject:
Field Theory and Polynomials
Subject:
Several Complex Variables and Analytic Spaces
Subject:
Mathematics-Algebraic Geometry
Copyright:
Edition Number:
1
Edition Description:
Book
Series:
Progress in Mathematics
Series Volume:
226
Publication Date:
20031114
Binding:
HARDCOVER
Language:
English
Illustrations:
Y
Pages:
303
Dimensions:
235 x 155 mm 1340 gr

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Related Subjects

Reference » Science Reference » General
Science and Mathematics » Mathematics » Algebra » Abstract Algebra
Science and Mathematics » Mathematics » Algebra » General
Science and Mathematics » Mathematics » Calculus » General
Science and Mathematics » Mathematics » Geometry » Algebraic Geometry
Science and Mathematics » Mathematics » Number Theory

Arithmetic of Higher-dimensional Algebraic Varieties New Hardcover
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$209.75 In Stock
Product details 303 pages Birkhauser - English 9780817632595 Reviews:
"Synopsis" by , 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.
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