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Arithmetic and Geometry – Ten Years in Alpbach (AMS-202) - Princeton Scholarship Online
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Arithmetic and Geometry: Ten Years in Alpbach (AMS-202)

Gisbert Wüstholz and Clemens Fuchs

Abstract

This book 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 heights 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 contains recent r ... More

Keywords: algebraic geometry, Shimura varieties, generalized Jacobians, hyperelliptic continued fractions, Faltings heights, L-functions, Langlands conjecture, Pell equation, Chowla–Selberg formula, Colmez conjecture

Bibliographic Information

Print publication date: 2019 Print ISBN-13: 9780691193779
Published to Princeton Scholarship Online: May 2020 DOI:10.23943/princeton/9780691193779.001.0001

Authors

Affiliations are at time of print publication.

Gisbert Wüstholz, editor
Friedburg Institute for Advanced Studies

Clemens Fuchs, editor
Paris Lodron University of Salzburg

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Contents

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Front Matter

Chapter One Introduction

Gisbert Wüstholz and Clemens Fuchs

Chapter Three Hyperelliptic Continued Fractions and Generalized Jacobians: Minicourse Given by Umberto Zannier

Laura Capuano, Peter Jossen, Christina Karolus, and Francesco Veneziano