Haocheng Fan

collaborators

2 papers

math.NT2025

Irreducibility of Newton strata in Picard modular surfaces and split local Galois representations

Haocheng Fan

We show that for a Picard modular form, the existence of companion forms is equivalent to the splitting properties of the associated local Galois representation. This result is obt…

math.NT2025

On the cohomological dimension of Siegel modular varieties and the modularity of formal Siegel modular forms

Haocheng Fan

We prove that the coherent cohomological dimension of the Siegel modular variety $A_{g, I^}$ is at most $g (g + 1) /2 - 2$ for $g \geq 2$ . As a corollary, we show that the boundary of the…