Yuri Tschinkel's Books

Algebraic Number Theory and Algebraic Geometry

Papers Dedicated to A.N. Parshin on the Occasion of His Sixtieth Birthday

By: S. V. Vostokov,Yuri Zarhin

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Algebraic Number Theory and Algebraic Geometry

Papers Dedicated to A.N. Parshin on the Occasion of His Sixtieth Birthday

By: S. V. Vostokov,Yuri Zarhin

A. N. Parshin is a world-renowned mathematician who has made significant contributions to number theory through the use of algebraic geometry. Articles in this volume present new research and the latest developments in algebraic number theory and algebraic geometry and are dedicated to Parshin's sixtieth birthday. Well-known mathematicians contributed to this volume, including, among others, F. Bogomolov, C. Deninger, and G. Faltings. The book is intended for graduate students andresearch mathematicians interested in number theory, algebra, and algebraic geometry.

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Page Count

232

Publisher

American Mathematical Soc.

Published Date

ISBN 10

0821832670

ISBN 13

9780821832677

Geometric Methods in Algebra and Number Theory

By: Fedor Bogomolov,Yuri Tschinkel

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Geometric Methods in Algebra and Number Theory

By: Fedor Bogomolov,Yuri Tschinkel

* Contains a selection of articles exploring geometric approaches to problems in algebra, algebraic geometry and number theory * The collection gives a representative sample of problems and most recent results in algebraic and arithmetic geometry * Text can serve as an intense introduction for graduate students and those wishing to pursue research in algebraic and arithmetic geometry

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384

Publisher

Springer Science & Business Media

Published Date

ISBN 10

0817643494

ISBN 13

9780817643492

Cohomological and Geometric Approaches to Rationality Problems

New Perspectives

By: Fedor Bogomolov,Yuri Tschinkel

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Cohomological and Geometric Approaches to Rationality Problems

New Perspectives

By: Fedor Bogomolov,Yuri Tschinkel

Rationality problems link algebra to geometry, and the difficulties involved depend on the transcendence degree of $K$ over $k$, or geometrically, on the dimension of the variety. A major success in 19th century algebraic geometry was a complete solution of the rationality problem in dimensions one and two over algebraically closed ground fields of characteristic zero. Such advances has led to many interdisciplinary applications to algebraic geometry. This comprehensive book consists of surveys of research papers by leading specialists in the field and gives indications for future research in rationality problems. Topics discussed include the rationality of quotient spaces, cohomological invariants of quasi-simple Lie type groups, rationality of the moduli space of curves, and rational points on algebraic varieties. This volume is intended for researchers, mathematicians, and graduate students interested in algebraic geometry, and specifically in rationality problems. Contributors: F. Bogomolov; T. Petrov; Y. Tschinkel; Ch. Böhning; G. Catanese; I. Cheltsov; J. Park; N. Hoffmann; S. J. Hu; M. C. Kang; L. Katzarkov; Y. Prokhorov; A. Pukhlikov

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Page Count

316

Publisher

Springer Science & Business Media

Published Date

ISBN 10

0817649344

ISBN 13

9780817649340

Rational Points on Algebraic Varieties

Zweite, aktualisierte und erweiterte Auflage

By: Emmanuel Peyre,Yuri Tschinkel

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Rational Points on Algebraic Varieties

Zweite, aktualisierte und erweiterte Auflage

By: Emmanuel Peyre,Yuri Tschinkel

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.

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Page Count

474

Publisher

Springer Science & Business Media

Published Date

ISBN 10

3764366125

ISBN 13

9783764366124

Algebra, Arithmetic, and Geometry

Volume I: In Honor of Yu. I. Manin

By: Yuri Tschinkel,Yuri Zarhin

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Algebra, Arithmetic, and Geometry

Volume I: In Honor of Yu. I. Manin

By: Yuri Tschinkel,Yuri Zarhin

EMAlgebra, Arithmetic, and Geometry: In Honor of Yu. I. ManinEM consists of invited expository and research articles on new developments arising from Manin’s outstanding contributions to mathematics.

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Page Count

723

Publisher

Springer Science & Business Media

Published Date

ISBN 10

0817647457

ISBN 13

9780817647452

Algebra, Arithmetic, and Geometry

Volume II: In Honor of Yu. I. Manin

By: Yuri Tschinkel,Yuri Zarhin

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Algebra, Arithmetic, and Geometry

Volume II: In Honor of Yu. I. Manin

By: Yuri Tschinkel,Yuri Zarhin

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Page Count

700

Publisher

Springer Science & Business Media

Published Date

ISBN 10

0817647473

ISBN 13

9780817647476

Eisenstein Series and Applications

By: Wee Teck Gan,Stephen S. Kudla,Yuri Tschinkel

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Eisenstein Series and Applications

By: Wee Teck Gan,Stephen S. Kudla,Yuri Tschinkel

Eisenstein series are an essential ingredient in the spectral theory of automorphic forms and an important tool in the theory of L-functions. They have also been exploited extensively by number theorists for many arithmetic purposes. Bringing together contributions from areas which do not usually interact with each other, this volume introduces diverse users of Eisenstein series to a variety of important applications. With this juxtaposition of perspectives, the reader obtains deeper insights into the arithmetic of Eisenstein series. The central theme of the exposition focuses on the common structural properties of Eisenstein series occurring in many related applications.

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Page Count

317

Publisher

Springer Science & Business Media

Published Date

ISBN 10

0817646396

ISBN 13

9780817646394

Algebra, Arithmetic, and Geometry

Volume II: In Honor of Yu. I. Manin

By: Yuri Tschinkel,Yuri Zarhin

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Algebra, Arithmetic, and Geometry

Volume II: In Honor of Yu. I. Manin

By: Yuri Tschinkel,Yuri Zarhin

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704

Publisher

Birkhäuser

Published Date

ISBN 10

0817647465

ISBN 13

9780817647469

Arithmetic of Higher-Dimensional Algebraic Varieties

By: Bjorn Poonen,Yuri Tschinkel

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Arithmetic of Higher-Dimensional Algebraic Varieties

By: Bjorn Poonen,Yuri Tschinkel

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.

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Page Count

308

Publisher

Springer Science & Business Media

Published Date

ISBN 10

081763259X

ISBN 13

9780817632595

Algebra, Arithmetic, and Geometry

Volume I: In Honor of Yu. I. Manin

By: Yuri Tschinkel,Yuri Zarhin

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Algebra, Arithmetic, and Geometry

Volume I: In Honor of Yu. I. Manin

By: Yuri Tschinkel,Yuri Zarhin

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Page Count

698

Publisher

Birkhäuser

Published Date

ISBN 10

0817647449

ISBN 13

9780817647445

Algebra, Arithmetic, and Geometry

By: Yuri Tschinkel,Yuri Zarhin

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Algebra, Arithmetic, and Geometry

By: Yuri Tschinkel,Yuri Zarhin

The two volumes of ""Algebra, Arithmetic, and Geometry: In Honor of Y.I. Manin"" are composed of invited expository articles and extensions detailing Manin's contributions to the subjects, and are in celebration of his 70th birthday. The well-respected and distinguished contributors include: Behrend, Berkovich, Bost, Bressler, Calaque, Carlson, Chambert-Loir, Colombo, Connes, Consani, Dabrowski, Deninger, Dolgachev, Donaldson, Ekedahl, Elsenhans, Enriques, Etingof, Fock, Friedlander, Geemen, Getzler, Goncharov, Harris, Iskovskikh, Jahnel, Kaledin, Kapranov, Katz, Kaufmann, Kollar, Kontsevich,

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Page Count

716

Publisher

Springer

Published Date

ISBN 10

0817672362

ISBN 13

9780817672362

Book's by Yuri Tschinkel

Algebraic Number Theory and Algebraic Geometry

Algebraic Number Theory and Algebraic Geometry

Geometric Methods in Algebra and Number Theory

Geometric Methods in Algebra and Number Theory

Cohomological and Geometric Approaches to Rationality Problems

Cohomological and Geometric Approaches to Rationality Problems

Rational Points on Algebraic Varieties

Rational Points on Algebraic Varieties

Algebra, Arithmetic, and Geometry

Algebra, Arithmetic, and Geometry

Algebra, Arithmetic, and Geometry

Algebra, Arithmetic, and Geometry

Eisenstein Series and Applications

Eisenstein Series and Applications

Algebra, Arithmetic, and Geometry

Algebra, Arithmetic, and Geometry

Arithmetic of Higher-Dimensional Algebraic Varieties

Arithmetic of Higher-Dimensional Algebraic Varieties

Algebra, Arithmetic, and Geometry

Algebra, Arithmetic, and Geometry

Algebra, Arithmetic, and Geometry

Algebra, Arithmetic, and Geometry

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