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Arithmetic and geometry :ten years i...

Fuchs, Clemens,

Arithmetic and geometry :ten years in alpbach /

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Arithmetic and geometry :edited by Gisbert Wüstholz and Clemens Fuchs.
其他題名:	ten years in alpbach /
其他作者:	Wüstholz, Gisbert,
面頁冊數:	1 online resource (186 p.)
標題:	Arithmetical algebraic geometry.
電子資源:	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:

347677
Arithmetical algebraic geometry.
Index Terms--Genre/Form:

214472
Electronic books.

LC Class. No.: QA242.5

Dewey Class. No.: 516.35

Arithmetic and geometry :ten years in alpbach /
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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.
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