The Geometry of Fontaine--Laffaille modules

Abstract

Fontaine--Laffaille modules are linear algebra objects that correspond to certain mod-p Galois representations. These Fontaine--Laffaille modules together with fixed bases compatible with the filtration are parameterized by the variety U\GL_n, where U is the subgroup of GL_n consisting of the upper-triangular unipotent matrices. In this short lecture series, we introduce the geometry of U\GL_n, and interpret some representation theoretic properties in terms of geometric languages.