The asymptotic behavior of Frobenius direct images of rings of invariants

Mitsuyasu Hashimoto, Peter Symonds

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)


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
Number of pages21
JournalAdvances in Mathematics
Publication statusPublished - Jan 10 2017


  • F-signature
  • Frobenius direct image
  • Frobenius limit
  • Hilbert–Kunz multiplicity

ASJC Scopus subject areas

  • Mathematics(all)


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