عنوان

Arithmetic and geometry :

(Number (ISBN

0691197547

(Number (ISBN

9780691197548

Erroneous ISBN

9780691193779

Erroneous ISBN

9780691193786

Title Proper

Arithmetic and geometry :

General Material Designation

[Book]

Other Title Information

ten years in Alpbach /

First Statement of Responsibility

edited by Gisbert Wüstholz and Clemens Fuchs.

Place of Publication, Distribution, etc.

Princeton :

Name of Publisher, Distributor, etc.

Princeton University Press,

Date of Publication, Distribution, etc.

2019.

Specific Material Designation and Extent of Item

1 online resource (viii, 174 pages)

Series Title

Annals of mathematics studies ;

Volume Designation

number 202

Text of Note

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.

Source for Acquisition/Subscription Address

JSTOR

Stock Number

22573/ctvft8mx7

Title

Arithmetic and Geometry : Ten Years in Alpbach (AMS-202).

International Standard Book Number

9780691193786

Arithmetical algebraic geometry, Congresses.

Arithmetical algebraic geometry.

Number

Edition

Class number

Book number

Fuchs, Clemens,1976-

Wüstholz, Gisbert

Date of Transaction

20200822123237.0

Cataloguing Rules (Descriptive Conventions))

rda

Electronic name

[Book]

Y