Year: 2026
Type: preprint
Abstract: We show that, in equal characteristic $p$, the Hodge-Witt polygon can only move down and domino numbers can only increase under specialization in smooth proper families. We also show that the Hodge polygon of the generic fiber of a proper smooth $p$-adic formal scheme over $\mathcal{O}_C$ lies on or above the Hodge-Witt polygon of its special fiber, where $C$ is a complete algebraically closed extension of $\mathbb{Q}_p$. We further show that, in this mixed-characteristic setting, if the crystalline cohomology of the special fiber is torsion-free in degrees $n$ and $n+1$, then the degree-$n$ Hodge polygon of the generic fiber lies on or below the abstract Hodge polygon of the special fiber. We illustrate these comparisons with explicit examples.
Source: arXiv (Cornell University)
Author: Yang, Yuan
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7220869595