L-invariants, completed cohomology and big principal series

Abstract: Let $f$ be a newform of weight $2$ that is Steinberg at $p$. Darmon showed that the Fontaine-Mazur $L$-invariant of the associated local $p$-adic Galois representation can be computed in terms of the cohomology of $p$-arithmetic subgroups of the group $PGL_2(\mathbb{Q})$. On the other hand Breuil showed that one can compute the $f$-isoyptical part of completed cohomology of the modular curve in terms of the cohomology of $p$-arithmetic groups. In this talk I will give generalizations of both results to higher rank reductive groups. This is partly joint work with Giovanni Rosso.

number theory

Audience: researchers in the topic

London number theory seminar

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For a record of talks predating this website see: wwwf.imperial.ac.uk/~buzzard/LNTS/numbtheo_past.html