Introduction

Course Meeting Times: TBD, roughly once every two weeks

Objective:

• Modular curves
• Elliptic curves over finite fields
• Understand the proof of Tate’s paper Endomorphisms of Abelian Varieties over Finite Fields
• Adelic constructions and its moduli interpretation

If time runs out, we will continue these topics by spring quarter.

Course Structure

Module 1: Modular curves

• Review: Introduction to modular curves and endomorphisms of elliptic curves
• Select chapters from Ribet-Stein
• References:

Module 2: EC over finite fields

• Number of rational points
• Weil conjectures
• Endomorphism ring
• Hasse invariant
• References:

Module 3: Tate’s paper