Rational Points on Algebraic Varieties.pdf

Rational Points on Algebraic Varieties

This book is devoted to the study of rational and integral points on higher dimensional algebraic varieties. It contains research papers addressing the arithmetic geometry of varieties which are not of general type, with an em phasis on how rational points are distributed with respect to the classical, Zariski and adelic topologies. The book gives a glimpse of the state of the art of this rapidly expanding domain in arithmetic geometry. The techniques involve explicit geometric con structions, ideas from the minimal model program in algebraic geometry as well as analytic number theory and harmonic analysis on adelic groups. In recent years there has been substantial progress in our understanding of the arithmetic of algebraic surfaces. Five papers are devoted to cubic surfaces: Basile and Fisher study the existence of rational points on certain diagonal cubics, Swinnerton-Dyer considers weak approximation and Broberg proves upper bounds on the number of rational points on the complement to lines on cubic surfaces. Peyre and Tschinkel compare numerical data with conjectures concerning asymptotics of rational points of bounded height on diagonal cubics of rank ~ 2. Kanevsky and Manin investigate the composition of points on cubic surfaces. Satge constructs rational curves on certain Kummer surfaces. Colliot-Thelene studies the Hasse principle for pencils of curves of genus 1. In an appendix to this paper Skorobogatov produces explicit examples of Enriques surfaces with a Zariski dense set of rational points.

Rational Points on Algebraic Varieties von … Rational Points on Algebraic Varieties von Emmanuel Peyre, Yuri Tschinkel (ISBN 978-3-0348-9536-1) bestellen. Schnelle Lieferung, auch auf Rechnung - lehmanns.de

3034895364 ISBN
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Rational Points on Algebraic Varieties.pdf


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Rational Points on Algebraic Varieties by Emmanuel Peyre, 9783764366124, available at Book Depository with free delivery worldwide. Counting Rational Points on Algebraic Varieties

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Rational Points on Algebraic Varieties von …

Noel Schulze

In number theory and algebraic geometry, a rational point of an algebraic variety is a point whose coordinates belong to a given field. If the field is not mentioned ... Oct 4, 2017 ... Algebraic geometry (e.g., [Har77]: up to Chapter II, §8 as a minimum, ... tions, in which it is the height of rational points that descends in the ...

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13.12.2017 · Understanding rational points on arbitrary algebraic varieties is the ultimate challenge. We have conjectures but few results. Poonen's book, with its mixture of basic constructions and openings into current research, will attract new generations to the Queen of Mathematics.-- Jean-Louis Colliot-Thélène, Université Paris-Sud Rational Points on Algebraic Varieties: Zweite ...