Higher Dimensional Varieties And Rational Points
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Author | : K. Böröczky |
Publisher | : Springer Science & Business Media |
Total Pages | : 322 |
Release | : 2003-07-10 |
Genre | : Mathematics |
ISBN | : 9783540008200 |
Exploring the connections between arithmetic and geometric properties of algebraic varieties has been the object of much fruitful study for a long time, especially in the case of curves. The aim of the Summer School and Conference on "Higher Dimensional Varieties and Rational Points" held in Budapest, Hungary during September 2001 was to bring together students and experts from the arithmetic and geometric sides of algebraic geometry in order to get a better understanding of the current problems, interactions and advances in higher dimension. The lecture series and conference lectures assembled in this volume give a comprehensive introduction to students and researchers in algebraic geometry and in related fields to the main ideas of this rapidly developing area.
Author | : Bjorn Poonen |
Publisher | : Springer Science & Business Media |
Total Pages | : 292 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 0817681701 |
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.
Author | : Károly Jr. Böröczky |
Publisher | : Springer Science & Business Media |
Total Pages | : 307 |
Release | : 2013-12-11 |
Genre | : Mathematics |
ISBN | : 3662051230 |
Exploring the connections between arithmetic and geometric properties of algebraic varieties has been the object of much fruitful study for a long time, especially in the case of curves. The aim of the Summer School and Conference on "Higher Dimensional Varieties and Rational Points" held in Budapest, Hungary during September 2001 was to bring together students and experts from the arithmetic and geometric sides of algebraic geometry in order to get a better understanding of the current problems, interactions and advances in higher dimension. The lecture series and conference lectures assembled in this volume give a comprehensive introduction to students and researchers in algebraic geometry and in related fields to the main ideas of this rapidly developing area.
Author | : Karoly Jr Boroczky |
Publisher | : |
Total Pages | : 316 |
Release | : 2014-09-01 |
Genre | : |
ISBN | : 9783662051245 |
Author | : Dmitri Kaledin |
Publisher | : IOS Press |
Total Pages | : 356 |
Release | : 2008 |
Genre | : Mathematics |
ISBN | : 1586038559 |
"Proceedings of the NATO Advanced Study Institute on Higher-Dimensional Geometry over Finite Fields, Geottingen, Germany, 25 June-6 July 2007."--T.p. verso.
Author | : Emmanuel Peyre |
Publisher | : Birkhäuser |
Total Pages | : 455 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 3034883684 |
This book is devoted to the study of rational and integral points on higher-dimensional algebraic varieties. It contains carefully selected research papers addressing the arithmetic geometry of varieties which are not of general type, with an emphasis on how rational points are distributed with respect to the classical, Zariski and adelic topologies. The present volume gives a glimpse of the state of the art of this rapidly expanding domain in arithmetic geometry. The techniques involve explicit geometric constructions, ideas from the minimal model program in algebraic geometry as well as analytic number theory and harmonic analysis on adelic groups.
Author | : Bjorn Poonen |
Publisher | : American Mathematical Soc. |
Total Pages | : 358 |
Release | : 2017-12-13 |
Genre | : Mathematics |
ISBN | : 1470437732 |
This book is motivated by the problem of determining the set of rational points on a variety, but its true goal is to equip readers with a broad range of tools essential for current research in algebraic geometry and number theory. The book is unconventional in that it provides concise accounts of many topics instead of a comprehensive account of just one—this is intentionally designed to bring readers up to speed rapidly. Among the topics included are Brauer groups, faithfully flat descent, algebraic groups, torsors, étale and fppf cohomology, the Weil conjectures, and the Brauer-Manin and descent obstructions. A final chapter applies all these to study the arithmetic of surfaces. The down-to-earth explanations and the over 100 exercises make the book suitable for use as a graduate-level textbook, but even experts will appreciate having a single source covering many aspects of geometry over an unrestricted ground field and containing some material that cannot be found elsewhere.
Author | : Carlo Gasbarri |
Publisher | : |
Total Pages | : 165 |
Release | : 2015 |
Genre | : Algebraic varieties |
ISBN | : 9781470428419 |
Author | : Bjorn Poonen |
Publisher | : Springer Science & Business Media |
Total Pages | : 308 |
Release | : 2004 |
Genre | : Mathematics |
ISBN | : 9780817632595 |
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.
Author | : Fedor Bogomolov |
Publisher | : Springer Science & Business Media |
Total Pages | : 324 |
Release | : 2013-05-17 |
Genre | : Mathematics |
ISBN | : 146146482X |
This book features recent developments in a rapidly growing area at the interface of higher-dimensional birational geometry and arithmetic geometry. It focuses on the geometry of spaces of rational curves, with an emphasis on applications to arithmetic questions. Classically, arithmetic is the study of rational or integral solutions of diophantine equations and geometry is the study of lines and conics. From the modern standpoint, arithmetic is the study of rational and integral points on algebraic varieties over nonclosed fields. A major insight of the 20th century was that arithmetic properties of an algebraic variety are tightly linked to the geometry of rational curves on the variety and how they vary in families. This collection of solicited survey and research papers is intended to serve as an introduction for graduate students and researchers interested in entering the field, and as a source of reference for experts working on related problems. Topics that will be addressed include: birational properties such as rationality, unirationality, and rational connectedness, existence of rational curves in prescribed homology classes, cones of rational curves on rationally connected and Calabi-Yau varieties, as well as related questions within the framework of the Minimal Model Program.