|Responsables :||Ziyang Gao, Marc Hindry, Bruno Kahn, João Pedro P. dos Santos|
|Email des responsables :||firstname.lastname@example.org|
|Orateur(s)||Alexander Betts - MPIM,|
|Titre||Weight--Monodromy and Canonical Paths on Varieties|
|Horaire||14:00 à 15:00|
We discuss an analogue of Deligne's weight-monodromy conjecture for the pro-unipotent fundamental groupoids of smooth varieties over mixed characteristic local fields, proved in the l=p case by Vologodsky and in general in joint work with Daniel Litt. One surprising consequence of this is that any two points in a smooth variety are connected by a canonical choice of "path". Time permitting, we will explain how, in the case of curves, these canonical paths admit a combinatorial description in terms of the reduction graph. This leads to a theory of refined Selmer varieties, and has consequences for the Chabauty-Kim method.
|Salle||salle 502, couloir 15-25|