Local stability of Frobenius and Artin--Schreier base-change: a comparison

Abstract

Let $(X,\Delta )\to C$ be a family of pairs over a smooth curve in positive characteristic $p>0$. We study the discrepancies of divisors over the base-change $(X,\Delta )\to C$ along Artin--Schreier and Frobenius covers of $C$, through ramification data for Artin--Schreier and degree $p$ purely inseparable extensions of DVRs. As an application, we recover a result of Hu and Zong about permanence of local stability for such base-change.

16 pages, comments are welcome. v2: Minor corrections