Project Details
Projekt
Images of Galois representations and deformations (B04)
Subject Area
Mathematics
Term
since 2021
Project identifier
Deutsche Forschungsgemeinschaft (DFG) - Project number 444845124
Locally, over p-adic fields we shall construct minimally ramified deformation rings for ℓ-adic representations for ℓ≠p, and classify irreducible mod p representations for ℓ=p, in both cases valued in reductive groups. Motivated by the Bloch–Kato conjecture for the adjoint motive of automorphic forms, certain invariants and the Cohen–Macaulayness of local deformation rings will be studied, and some new modularity results shall be explored. A further focus on the global side are p-adic families and compatible systems of automorphic Galois representations with conjugate self-twists valued in GL(n), as well as an analog of a conjecture for Greenberg for GSp(4). Related abstract big image questions lead naturally to particular questions on group cohomology.
DFG Programme
CRC/Transregios
Applicant Institution
Goethe-Universität Frankfurt am Main
Project Head
Professor Dr. Gebhard Böckle
