## 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.