$K_1$-invariants in the mod $p$ cohomology of $U(3)$ arithmetic manifolds

Daniel Le, Bao Viet Le Hung, Stefano Morra

Let $F/F^{+}$ be a CM extension and $H_{/F^{+}}$ a definite unitary group in three variables that splits over $F$. We describe Hecke isotypic components of mod $p$ algebraic modular fo…