Base-change of locally stable families in positive characteristic

2026/07/24 by Marta Benozzo, Quentin Posva
Mathematics · #math.AG

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Abstract

We investigate the permanence of local stability for one-parameter families X→ 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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