Year: 2008
Type: preprint
Abstract: We propose in this paper an approach to Breuil's conjecture on a Langlands correspondence between $p$-adic Galois representations and representations of $p$-adic Lie groups in $p$-adic topological vector spaces. We suggest that Berthelot's theory of arithmetic $D$-modules should give a $p$-adic analogue of Kashiwara's theory of $D$-modules for real Lie groups i.e. it should give a realization of the $p$-adic representations of a $p$-adic Lie group as spaces of overconvergent solutions of arithmetic $D$-modules which will come equipped with an action of the Galois group. We shall discuss the case of Siegel modular varieties as a possible testing ground for the proposal.
Source: arXiv (Cornell University)
Author: Lai, King Fai
Institution: Institut de recherche mathématique de Rennes
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4385713694