Explicitly Extending Frobenius Splittings over Finite Maps

Abstract

Suppose that π: Y → 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.

Key Words:

• Finite map
• Frobenius splitting
• Ramification divisor
• Separable map
• Tame ramification

2010 Mathematics Subject Classification:

• 14B05
• 13A35
• 14F18

ACKNOWLEDGMENTS

The authors would like to thank Karen Smith for several inspiring discussions.

Notes

Communicated by L. Ein.