SERRE WEIGHTS AND BREUIL’S LATTICE CONJECTURE IN DIMENSION THREE
SERRE WEIGHTS AND BREUIL’S LATTICE CONJECTURE IN DIMENSION THREE
We prove in generic situations that the lattice in a tame type induced by the completed cohomology of a $U(3)$ -arithmetic manifold is purely local, that is, only depends on the Galois representation at places above $p$ . This is a generalization to $\text{GL}_{3}$ of the lattice conjecture of Breuil. …