Smooth modular representation theory of p-adic reductive groups

• Applicant: Professor Dr. Jan Kohlhaase
• Subject Area: Mathematics
• Term: since 2020
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 435414187

The Langlands program is one of the most influential driving forces in modern mathematics. Our research project is concerned with the young variant of the local Langlands program in characteristic p. During the first funding period we have shown how the theory of model categories can be applied fruitfully to the study of smooth representations of p-adic reductive groups in characteristic p. In particular, we generalized an important result of Cabanes concerning finite reductive groups to the p-adic setting. Moreover, we could show how to pass from suitable coefficient systems on the Bruhat-Tits building to a dual theory of equivariant sheaves. This is another step towards a generalization of the theory of Schneider and Stuhler to the mod-p setting. During the second funding period we intend to develop our approaches further and apply them to questions related to the local Langlands program in characteristic p. In particular, this concerns Gorenstein derived categories, the computation of derived generators in homotopy categories of Hecke modules and the study of finiteness properties of generalized (phi,Gamma)-modules via compactifications of Bruhat-Tits buildings.

• DFG Programme: Research Grants