Chandrasekhar Hall

Steps to generalization of p-adic Langlands programme via multivariable (Phi, Gamma)-modules and applications

Aprameyo Pal

HRI

In the first half of the talk, I recall the motivation and construction for multivariable (Phi, Gamma)-modules in the context of the
emerging p-adic Langlands programme. In the second half of the talk (joint work—partly in progress with Gergely Zabradi), I show how to pass
to Robba-style versions via overconvergence. The group cohomology can also be computed from the generalized Herr complex over the multivariate
Robba ring. If time permits, I will indicate how the analytic Iwasawa cohomology (computed also from a generalized Herr-complex) will be
useful for the (re)formulation of Bloch-Kato exponential maps in this setting.