Sonstige Vorträge

Abstract

We generalize the DeBacker--Reeder/Kaletha construction of depth-0 supercuspidal L-packets to all tame covers defined by étale cohomology. This can be seen as the "regular depth-0" part of the local Langlands correspondence for covers. This talk is based on joint work with Nhat Hoang Le, which is in turn based on earlier works by Luozi Shi and myself.

By a connection with a formal parameter, we mean a connection on a scheme $X$ that is relatively smooth over the ring $R = k[[t]]$, where $k$ is a field of characteristic $0$. The monodromy of such a connection is a flat affine group scheme over $R$. We introduce the notion of prudent group schemes in terms of their representations; this property turns out to be equivalent to the projectivity of the coordinate ring (a result that holds over any complete DVR). In this talk, we discuss the question: When is the monodromy group of a connection prudent? Our main tool is the concept of hyper-prudence, which involves the $t$-adic completion of the representation category. This is a joint work with J.P. dos Santos (Montpellier) and Dao Van Thinh, Pham Thanh Tam (Hanoi).

We invite all early career researchers who have started their position at Mathematics Münster in 2026 to join us for a welcoming Meet&Greet session with the Cluster spokespersons, some investigators, the MM management staff and all the new members.