Number Theory Seminar
In this lecture, we are interested in using group-theoretic information to derive consequences for tamely ramified Galois representations of number fields. I will present two recent results giving some new evidence for the Tame Fontaine--Mazur conjecture.
The first one is an extension of the strategy of Boston from the '90s by studying the fixed points of a semi-simple action on a $p$-adic Lie group (joint work with Farshid Hajir). The second one concerns the unramified version and the case where $p=2$. By comparing the cohomology of the studied objects, one obtains many new situations for which the unramified version of the FM conjecture holds; in particular, for imaginary quadratic fields!