L-invariants and p-adic automorphic forms in ranks 2 and 3

• Applicant: Dr. Peter Mathias Gräf
• Subject Area: Mathematics
• Term: from 2021 to 2024
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 491064713

In this project several important questions centered on L-invariants and p-adic automorphic forms for GL2 and GL3 shall be investigated. The first central goal is to explore relations between the ghost conjecture of Bergdall-Pollack and conjectures on valuations of L-invariants, both computationally and theoretically. The second goal is to prove a new non-criticality statement for certain p-adic automorphic forms for GL3 over p-adic fields, which implies an analogue of the well-known theorem of Amice-Vélu and Vishik. This in turn can be used to achive the third goal of this proposal: the construction of Teitelbaum-style L-invariants in the rank-3 situation for forms of higher weight.

• DFG Programme: WBP Fellowship
• International Connection: USA
• Host: Professor Dr. Robert Pollack