Let `$K$`

be a finite extension of `$\mathbb{Q}_p$`

. The theory of `$(\varphi, \Gamma)$`

-modules constructed by Fontaine provides a good category to study `$p$`

-adic representations of the absolute Galois group `$Gal(\bar{K}/K)$`

. This theory arises from a ‘‘devissage’’ of the extension `$\bar{K}/K$`

through an intermediate extension `$K_{\infty}/K$`

which is the cyclotomic extension of `$K$`

. The notion of `$(\varphi, \tau)$`

-modules generalizes Fontaine’s constructions by using Kummer extensions other than the cyclotomic one. It encapsulates the important notion of Breuil-Kisin modules among others. It is thus desirable to establish properties of `$(\varphi, \tau)$`

-modules parallel to the cyclotomic case. In this talk, we explain the construction of a functor that associates to a family of `$p$`

-adic Galois representations a family of `$(\varphi, \tau)$`

-modules. The analogous functor in the `$(\varphi, \Gamma)$`

-modules case was constructed by Berger and Colmez . This is joint work with Leo Poyeton.

- All seminars.
- Seminars for 2021

Last updated: 03 Feb 2023