# Workshop: Arithmetic intersection theory and Shimura varieties

Supported by the SFB Transregio 45 "Periods, moduli spaces and arithmetic of algebraic varieties"

**Date:** February 3 - 7, 2014

**Venue:** HIM lecture hall, Poppelsdorfer Allee 45

**Organizers:** Dennis Eriksson, Siddarth Sankaran, Giuseppe Ancona, Gerard Freixas, Javier Fresán, Marc-Hubert Nicole

The aim of this workshop was to study the interactions of the following topics:

- Arakelov theory
- Shimura varieties and automorphic forms
- p-adic analytic geometry

It was part of the activities organized by the working group "p-adic methods in Arakelov geometry and Shimura varieties" during the junior Hausdorff trimester program "Algebraic geometry". Arakelov theory is a framework to study the geometry of arithmetic varieties by finding analogies to complex geometry. In particular it provides an intersection theory for schemes defined over the ring of integers of a number field. This theory has found remarkable applications to the study of arithmetic cycles on Shimura varieties, such as in Kudla's programme that seeks to relate generating series of intersection numbers of such cycles to the Fourier coefficients of modular forms.

On the other hand, recent developments in p-adic analytic geometry, such as Berkovich spaces, suggest new approaches to Arakelov geometry by drawing on analogies from complex differential geometry.

One of the key aims of this conference was to assemble experts from all these fields to discuss these new developments and their ramifications in the context of Shimura varieties.

Speakers: Fabrizio Andreatta, Massimo Bertolini, Amnon Besser, Jean-Benoît Bost, José Ignacio Burgos, Daniel Disegni, Walter Gubler, Ben Howard, Jürg Kramer, Klaus Künnemann, Matteo Longo, Anna-Maria von Pippich, Martin Raum, Michael Rapoport, Damian Rössler, Peter Scholze, Maryna Viazoska, Eva Viehmann, Tonghai Yang, Don Zagier