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.

About the Author

Gisbert W�stholz is professor emeritus of mathematics at ETH Zurich. Clemens Fuchs is professor of discrete mathematics at the University of Salzburg.

"About this title" may belong to another edition of this title.

Store Description

We carry a comprehensive range of out of print and rare books.

Visit Seller's Storefront

Seller's business information

Kennys Bookshops and Art Galleries Limited
Liosban Industrial Estate, Tuam Road, Galway, GY, Ireland

Sale & Shipping Terms

Terms of Sale

We guarantee the condition of every book as it's described on the Abebooks websites.

If you're dissatisfied with your purchase (Incorrect Book/Not as Described/Damaged) or if the order hasn't arrived, you're eligible for a refund within 30 days of the estimated delivery date.

For any queries please use the contact seller link or send an email to books@kennys.ie

Conor Kenny

Shipping Terms

All books securely packaged. Some books ship from Ireland.

Shipping rates within U.S.A.

Shipping rates within U.S.A.
Order quantity	14 to 20 business days	13 to 14 business days
First item	US$ 10.50	US$ 21.00

Delivery times are set by sellers and vary by carrier and location. Orders passing through Customs may face delays and buyers are responsible for any associated duties or fees. Sellers may contact you regarding additional charges to cover any increased costs to ship your items.