| Résume | The Breuil--Mézard conjecture is a numerical shadow of the hypothetical $p$-adic Langlands correspondence, which roughly describes the mod $p$ geometry of spaces of local Galois representations with $p$-adic Hodge theoretic conditions in terms of modular representation theory of finite groups. In this talk, I will recall the geometric formulation of the conjecture, and explain the proof of some new cases for small Hodge--Tate weights. This is joint work in progress with Shun Yin. |
