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arXiv · 2607.22106

Base-change of locally stable families in positive characteristic

Marta Benozzo·Quentin Posva
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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.

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Marta Benozzo, Quentin Posva. 2026-08-28. Base-change of locally stable families in positive characteristic. https://arxiv.org/abs/2607.22106

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