On the behavior of $F$-signatures, splitting primes, and test modules under finite covers

Abstract

We give a comprehensive treatment on how $F$-signatures, splitting primes, splitting ratios, and test modules behave under finite covers. To this end, we expand on the notion of transposability along a section section of the relative canonical module as first introduced by K.~Schwede and K.~Tucker.

arXiv comment39 pages, comments are more than welcome. v3: major revision: shortened proofs and sharpened results v4: improved exposition, final version

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Cited by in corpus (4)

• An analog of adjoint ideals and PLT singularities in mixed characteristic
• Tame fundamental groups of pure pairs and Abhyankar's lemma
• Inversion of adjunction for $F$-signature
• On tame ramification and centers of $F$-purity