Park City lectures on elliptic curves over function fields

2011/01/10 by Douglas Ulmer, Ulmer, Douglas · 1 citation
Mathematics · #11G05 #11G40 #14H25 #14J27 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT) #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.1101.1939

openalex publication_date 2011/01/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

These are the notes from a course of five lectures at the 2009 Park City Math Institute. The focus is on elliptic curves over function fields over finite fields. In the first three lectures, we explain the main classical results (mainly due to Tate) on the Birch and Swinnerton-Dyer conjecture in this context and its connection to the Tate conjecture about divisors on surfaces. This is preceded by a "Lecture 0" on background material. In the remaining two lectures, we discuss more recent developments on elliptic curves of large rank and constructions of explicit points in high rank situations.

Citations

• Good Reduction of Abelian Varieties
• The Criteria for Algebraic Equivalence and the Torsion Group

Cited by

• A Unified Finiteness Theorem For Curves Over Function Fields

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