On Base Change of Local Stability in Positive Characteristics

Abstract

We prove that a pointed one dimensional family of varieties $\mathcal{X}\to b\in B$ in positive characteristics is locally stable iff the log pair $({\mathcal{X}}^{\prime },{\mathcal{X}}_{b^{\prime }}^{\prime })$ arising from its base change to the perfectoid base $b^{\prime }\in B_{perf}$ is log canonical.

12pages