Arithmetic Intersections

Lecturer Dr. Andreas Mihatsch
Email mihatsch (add ''at''math.uni-bonn.de)
Office Room 4.024

Lecture Mon 14:15 -- 15:45, in room 1.008
1st lecture on Apr 4
No lectures Apr 18, May 23, June 6, July 11


Lecture notes

Latest version (updated June 27)


Contents

The Gross--Zagier formula relates derivatives of L-functions with the torsion property of points on elliptic curves. A systematic approach to this statement is through a comparison of relative trace formulas. It leads to an Arithmetic Fundamental Lemma (AFL) identity for the group GL_2. This is an identity that involves intersection numbers on the modular curve and orbital integrals.

The aim of course is to understand the proof and context of this AFL identity.


Prerequisites

  • Firm knowledge of algebraic geometry, e.g. from the courses AG 1 and 2
  • Algebraic number theory
  • Some background in arithmetic geometry, e.g. for etale cohomology, curves or abelian varieties

Exams

During the weeks August 8--12 and September 26--30.