PreprintCC BY 4.0arXiv
Base-change of locally stable families in positive characteristic
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,Xc), 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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BibTeX
@misc{benozzo2026basechange,
title = {{Base-change of locally stable families in positive characteristic}},
author = {Marta Benozzo and Quentin Posva},
howpublished = {arXiv},
year = {2026},
month = aug,
doi = {10.48550/arxiv.2607.22106},
eprint = {2607.22106},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2607.22106},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Base-change of locally stable families in positive characteristic
AU - Marta Benozzo
AU - Quentin Posva
PY - 2026
DA - 2026/08/28
PB - arXiv
DO - 10.48550/arxiv.2607.22106
UR - https://arxiv.org/abs/2607.22106
AB - 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.
ER -