Year: 2026
Type: preprint
Abstract: We investigate the permanence of local stability for one-parameter families $X\to C$ under finite flat base-changes, when the base-field has positive characteristic $p>0$. Building on previous work of Hu--Zong, we show that it suffices to consider base-changes by Frobenius morphisms. In that case, we show that the situation is governed by the discrepancies of the pairs $(X,X_c)$, together with some differential invariants of the vertical divisors whose multiplicity in their fiber is divisible by $p$. While the behaviour of these invariants remains in general mysterious, we establish upper bounds under some $F$-splitting assumptions.
Source: arXiv (Cornell University)
Authors: Benozzo, Marta, Posva, Quentin
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7171389432