Xiangsheng Wei: Moduli stack of p-adic representation of the product of Galois group

Nowadays there are two main approaches to defining (and study) of moduli stack of galois representations. On the one hand, one can define the moduli stack of the galois representations in a naive way (namely, consider the groupoid of continuous representations with coefficient $A$, for any $p$-adic ring $A$). But such approach behaves badly for families of representations. On the other hand, Emerton and Gee give a (seems successful) definition using $(\phi,\gamma)$-modules.

 

In this talk, I will generalize E-G stack to the multivariable case, which corresponds to the representations of the product of galois group(recall that products of galois groups appear naturally in the local Langlands conjectures). In particular, I will give a description of the moduli stack of one-dim representation and present some related results and questions. This is an ongoing work.