Arithmetic and Geometry : Ten Years in Alpbach.

Description

Cover Contents Preface 1. Introduction 2. Local Shimura Varieties: Minicourse Given by Peter Scholze 2.1 Introduction 2.2 Local Langlands Correspondence 2.3 Approach to LLC via Lubin-Tate Spaces 2.4 Approach to LLC via Rapoport-Zink Spaces 2.5 Some Basics of p-adic Geometry 2.6 Approach to LLC via Fargues-Fontaine Curve Bibliography 3. Hyperelliptic Continued Fractions and Generalized Jacobians: Minicourse Given by Umberto Zannier 3.1 Introduction and Some History 3.2 The Continued Fraction Expansion of Real Numbers 3.3 Continued Fractions in More General Settings 3.4 The Continued Fraction Expansion of Laurent Series3.5 Pell Equation in Polynomials 3.6 Distribution of Pellian Polynomials 3.7 The Pell Equation in the Nonsquarefree Case 3.8 A Skolem-Mahler-Lech Theorem for Algebraic Groups 3.9 Periodicity of the Degrees of the Partial Quotients 3.10 Solutions to the Exercises Bibliography 4. Faltings Heights and L-functions: Minicourse Given by Shou-Wu Zhang 4.1 Heights and L-functions 4.2 Shimura Curves and Averaged Colmez Conjecture 4.3 The Generalized Chowla-Selberg Formula 4.4 Higher Chowla-Selberg/Gross-Zagier Formula Bibliography