p-adic group rings play a central role in several areas of number theory, most prominently in the p-adic Langlands program and in Iwasawa theory. We plan to systematically develop derived methods in the p-adic Langlands program. First steps will be to understand the cohomology algebra of the previously constructed differential graded Hecke algebra and possibly to categorify the latter. In Iwasawa theory we will continue the investigation of Iwasawa cohomology with applications to regulator maps and reciprocity laws.
DFG Programme
Collaborative Research Centres
