The Asymptotic Behavior of Frobenius Direct Images of Rings of Invariants

Mitsuyasu Hashimoto, Peter Symonds

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    We define the Frobenius limit of a module over a ring of prime characteristic to be the limit of the normalized Frobenius direct images in a certain Grothendieck group. When a finite group acts on a polynomial ring, we calculate this limit for all the modules over the twisted group algebra that are free over the polynomial ring; we also calculate the Frobenius limit for the restriction of these to the ring of invariants. As an application, we generalize the description of the generalized F-signature of a ring of invariants by the second author and Nakajima to the modular case.
    Original languageEnglish
    Pages (from-to)144-164
    JournalAdvances in Mathematics
    Issue number0
    Early online date28 Sept 2016
    Publication statusE-pub ahead of print - 28 Sept 2016


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