Explicitly Extending Frobenius Splittings over Finite Maps

Suppose that $π\: Y \to X$ 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 $π$ is tamely ramified in codimension 1. Some additional examples are also explored.

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