On rational structures on automorphic representations and applications to special values of L-functions

Date
2015/07/24 Fri 13:30 - 14:30
Room
3号館152号室
Speaker
Fabian Januszewski
Affiliation
Karlsruhe Institute of Technology
Abstract

Since their invention four decades ago, modular symbols have been a powerful tool in the study of the arithmetic of special values of L-functions. Being defined purely cohomologically, modular symbols a priori only capture the rationality properties of the finite part of the underlying automorphic representation. In particular, in higher rank situations, it is not clear how cohomologically defined periods attached to different critical values are related. To overcome this issue, I will discuss the construction of rational structures on the archimedean part of automorphic representations which then induce global rational structures. In certain cases, where we know that certain functionals are rational themselves, these rational structures allow us to prove period relations as predicted by Deligne's Conjecture.