Pre-Alpbach Minicourse - Special cycles on Shimura curves

Andreas Mihatsch (Universität Bonn)

March 30, 16:00 - 18:00, HG G 19.2
March 31, 14:00 - 16:00, HG G 19.2
March 31, 17:00 - 19:00, HG G 19.2
April 01, 13:00 - 15:00, HG G 43

This is a preparation course for the Workshop "Special cycles on Shimura curves", taking place from July 5 to 10, 2014 in Alpbach, Austria.

Abstract

The mini-course is  an introduction into the topic of the Alpbach Summer School 2015 to take place in July 2015. There special cycles on Shimura curves attached to an indefinite quaternion algebra will be studied which will serve to define the Fourier expansion of an elliptic modular form of weight 3/2. This will then be turned into an arithmetic surfaces setting which leads to the Fourier expansion of a non-holomorphic modular form of weight 3/2 with values in an arithmetic Chow group attached to the underlying arithmetic surface.

Lecture 1: Introduction, Special cycles over C and their degrees

Lecture 2 & 3: Geometry of Shimura Curves and special cycles (p-adic uniformization)

Lecture 4: Generating series in Arithmetic Chow groups and its modularity.