On a torsion analogue of the weight-monodromy conjecture

TL;DR

This paper introduces and proves a torsion analogue of the weight-monodromy conjecture for various classes of algebraic varieties over non-archimedean local fields, extending understanding in arithmetic geometry.

Contribution

It formulates a torsion version of the weight-monodromy conjecture and proves it for several important classes of schemes over equal characteristic local fields.

Findings

Proved the conjecture for proper smooth schemes over equal characteristic fields

Established results for abelian varieties and surfaces

Extended to varieties uniformized by Drinfeld upper half spaces

Abstract

We formulate and study a torsion analogue of the weight-monodromy conjecture for a proper smooth scheme over a non-archimedean local field. We prove it for proper smooth schemes over equal characteristic non-archimedean local fields, abelian varieties, surfaces, varieties uniformized by Drinfeld upper half spaces, and set-theoretic complete intersections in toric varieties. In the equal characteristic case, our methods rely on an ultraproduct variant of Weil II established by Cadoret.