Project Details
Projekt
p-adic L-functions, L-invariants and the cohomology of arithmetic groups (B05)
Subject Area
Mathematics
Term
since 2023
Project identifier
Deutsche Forschungsgemeinschaft (DFG) - Project number 491392403
The Conjecture of Birch and Swinnerton-Dyer (BSD) and its generalizations predict that the vanishing of motivic L-functions controls the number of rational solutions of polynomial equations. Our most promising approach towards this conjecture is via its p-adic analogue, the p-adic BSD Conjecture. Here exceptional zeros and L-invariants occur as new phenomena and we will focus on these two aspects: We will formulate and prove results towards an Exceptional Zero Conjecture from an automorphic point of view. Our approach is based on the cohomology of arithmetic groups and infinitesimal deformations of local principal series representations. One of the challenges will be the identification of the correct L-invariant in this setting.
DFG Programme
CRC/Transregios
Applicant Institution
Universität Bielefeld
Project Heads
Professor Dr. Fabian Januszewski; Professor Dr. Michael Spieß
