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Arithmetic and geometry : = ten year...

Wüstholz, Gisbert,

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Arithmetic and geometry : = ten years in alpbach /

Record Type:	Electronic resources : Monograph/item
Title/Author:	Arithmetic and geometry :/ edited by Gisbert Wüstholz and Clemens Fuchs.
Reminder of title:	ten years in alpbach /
other author:	Wüstholz, Gisbert,
Description:	1 online resource (186 p.)
[NT 15003449]:	Arithmetic and geometry : ten years in alpbach -- Contents -- Preface -- Chapter 1. Introduction -- Chapter 2. Local Shimura Varieties: Minicourse Given by Peter Scholze -- Chapter 3. Hyperelliptic Continued Fractions and Generalized Jacobians: Minicourse Given by Umberto Zannier -- Chapter 4. Faltings Heights and L-functions: Minicourse Given by Shou-Wu Zhang -- List of Contributors.
Subject:	Arithmetical algebraic geometry. -
Online resource:	https://portal.igpublish.com/iglibrary/search/PUPB0007135.html
ISBN:	0691197547

Arithmetic and geometry : = ten years in alpbach /
Arithmetic and geometry :ten years in alpbach /edited by Gisbert Wüstholz and Clemens Fuchs. - 1st ed. - 1 online resource (186 p.) - Annals of mathematics studies. - Annals of mathematics studies..

Includes bibliographical references and index.

Arithmetic and geometry : ten years in alpbach -- Contents -- Preface -- Chapter 1. Introduction -- Chapter 2. Local Shimura Varieties: Minicourse Given by Peter Scholze -- Chapter 3. Hyperelliptic Continued Fractions and Generalized Jacobians: Minicourse Given by Umberto Zannier -- Chapter 4. Faltings Heights and L-functions: Minicourse Given by Shou-Wu Zhang -- List of Contributors.

Arithmetic and Geometry presents highlights of recent work in arithmetic algebraic geometry by some of the world's leading mathematicians. Together, these 2016 lectures-which were delivered in celebration of the tenth anniversary of the annual summer workshops in Alpbach, Austria-provide an introduction to high-level research on three topics: Shimura varieties, hyperelliptic continued fractions and generalized Jacobians, and Faltings height and L-functions. The book consists of notes, written by young researchers, on three sets of lectures or minicourses given at Alpbach. The first course, taught by Peter Scholze, contains his recent results dealing with the local Langlands conjecture. The fundamental question is whether for a given datum there exists a so-called local Shimura variety. In some cases, they exist in the category of rigid analytic spaces in others, one has to use Scholze's perfectoid spaces. The second course, taught by Umberto Zannier, addresses the famous Pell equation-not in the classical setting but rather with the so-called polynomial Pell equation, where the integers are replaced by polynomials in one variable with complex coefficients, which leads to the study of hyperelliptic continued fractions and generalized Jacobians. The third course, taught by Shou-Wu Zhang, originates in the Chowla–Selberg formula, which was taken up by Gross and Zagier to relate values of the L-function for elliptic curves with the height of Heegner points on the curves. Zhang, X. Yuan, and Wei Zhang prove the Gross–Zagier formula on Shimura curves and verify the Colmez conjecture on average.

Mode of access: World Wide Web.

ISBN: 0691197547Subjects--Topical Terms:

699672
Arithmetical algebraic geometry.
Index Terms--Genre/Form:

542853
Electronic books.

LC Class. No.: QA242.5

Dewey Class. No.: 516.35

Arithmetic and geometry : = ten years in alpbach /
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245 0 0 $a Arithmetic and geometry : $b ten years in alpbach / $c edited by Gisbert Wüstholz and Clemens Fuchs.
250 $a 1st ed.
264 1 $a Princeton : $b Princeton University Press, $c 2019.
300 $a 1 online resource (186 p.)
336 $a text $b txt $2 rdacontent
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490 1 $a Annals of mathematics studies
504 $a Includes bibliographical references and index.
505 0 $a Arithmetic and geometry : ten years in alpbach -- Contents -- Preface -- Chapter 1. Introduction -- Chapter 2. Local Shimura Varieties: Minicourse Given by Peter Scholze -- Chapter 3. Hyperelliptic Continued Fractions and Generalized Jacobians: Minicourse Given by Umberto Zannier -- Chapter 4. Faltings Heights and L-functions: Minicourse Given by Shou-Wu Zhang -- List of Contributors.
520 $a Arithmetic and Geometry presents highlights of recent work in arithmetic algebraic geometry by some of the world's leading mathematicians. Together, these 2016 lectures-which were delivered in celebration of the tenth anniversary of the annual summer workshops in Alpbach, Austria-provide an introduction to high-level research on three topics: Shimura varieties, hyperelliptic continued fractions and generalized Jacobians, and Faltings height and L-functions. The book consists of notes, written by young researchers, on three sets of lectures or minicourses given at Alpbach. The first course, taught by Peter Scholze, contains his recent results dealing with the local Langlands conjecture. The fundamental question is whether for a given datum there exists a so-called local Shimura variety. In some cases, they exist in the category of rigid analytic spaces in others, one has to use Scholze's perfectoid spaces. The second course, taught by Umberto Zannier, addresses the famous Pell equation-not in the classical setting but rather with the so-called polynomial Pell equation, where the integers are replaced by polynomials in one variable with complex coefficients, which leads to the study of hyperelliptic continued fractions and generalized Jacobians. The third course, taught by Shou-Wu Zhang, originates in the Chowla–Selberg formula, which was taken up by Gross and Zagier to relate values of the L-function for elliptic curves with the height of Heegner points on the curves. Zhang, X. Yuan, and Wei Zhang prove the Gross–Zagier formula on Shimura curves and verify the Colmez conjecture on average.
538 $a Mode of access: World Wide Web.
650 0 $a Arithmetical algebraic geometry. $3 699672
655 4 $a Electronic books. $2 lcsh $3 542853
700 1 $a Wüstholz, Gisbert, $e editor. $3 3440664
700 1 $a Fuchs, Clemens, $e editor. $3 3440665
830 0 $a Annals of mathematics studies. $3 751754
856 4 0 $u https://portal.igpublish.com/iglibrary/search/PUPB0007135.html