### arXiv:1509.02592 [math.AC]AbstractReferencesReviewsResources

#### The asymptotic behavior of Frobenius direct images of rings of invariants

Mitsuyasu Hashimoto, Peter Symonds

Published 2015-09-09Version 1

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.

**Comments:**25 pages

arXiv:1010.1606 [math.AC] (Published 2010-10-08)

Good filtrations and strong $F$-regularity of the ring of $U_P$-invariants

Asymptotic behavior of the socle of Frobenius powers

Rings of invariants for modular representations of the Klein four group