Explicitly Extending Frobenius Splittings over Finite Maps

Abstract

Suppose that $\pi Y\to X$ is a finite map of normal varieties over a perfect field of characteristic $p>0$. Previous work of the authors gave a criterion for when Frobenius splittings on $X$ (or more generally any $p^{-e}$-linear map) extend to $Y$. In this paper we give an alternate and highly explicit proof of this criterion (checking term by term) when $\pi$ is tamely ramified in codimension 1. Some additional examples are also explored.

8 pages, comments welcome

References in corpus (1)

• On the behavior of test ideals under finite morphisms