Monodromy results for abelian surfaces and K3 surfaces with bad reduction

TL;DR

This paper proves a p-adic monodromy theorem for certain algebraic surfaces with bad reduction and applies it to finiteness results for Hecke orbit reductions in supersingular cases.

Contribution

It establishes a local p-adic monodromy theorem for abelian surfaces and K3 surfaces with bad reduction, a novel result in this area.

Findings

Proves a p-adic monodromy theorem for these surfaces.

Shows finiteness of Hecke orbit reductions in supersingular cases.

Provides new insights into the reduction behavior of these surfaces.

Abstract

The purpose of this paper is to prove a local p-adic monodromy theorem for ordinary abelian surfaces and K3 surfaces with bad reduction in characteristic p. As an application, we get a finiteness result for the reduction of their Hecke orbits in the case of type II supersingular reduction.