# Séminaires : Séminaire Théorie des Nombres

 Equipe(s) : fa, tn, tga, Responsables : Marc Hindry, Bruno Kahn, Wieslawa Niziol, Cathy Swaenepoel Email des responsables : cathy.swaenepoel@imj-prg.fr Salle : Adresse : Description http://www.imj-prg.fr/tn/STN/stnj.html

 Orateur(s) Jędrzej Garnek - Institute of Mathematics of Polish Academy of Sciences, Titre HKG-curves and cohomologies of p-group covers Date 16/01/2023 Horaire 14:00 à 15:00 Diffusion Résume Let $k$ be an algebraically closed field of characteristic $p > 0$, and let $G$ be a finite $p$-group. The results of Harbater, Katz and Gabber associate to every action of $G$ on $k[[t]]$ a $G$-cover of the projective line ramified only over $\infty$. During this talk we will present a new way of computing cohomologies of HKG-covers. We apply this result to the classical problem of determining the equivariant structure of cohomologies of a curve with an action of a $p$-group. As an example, we compute the de Rham cohomology of Klein four covers. Salle 15-25-502 Adresse Jussieu