TY - JOUR

T1 - The asymptotic behavior of Frobenius direct images of rings of invariants

AU - Hashimoto, Mitsuyasu

AU - Symonds, Peter

N1 - Publisher Copyright:
© 2016 Elsevier Inc.

PY - 2017/1/10

Y1 - 2017/1/10

N2 - 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.

AB - 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.

KW - F-signature

KW - Frobenius direct image

KW - Frobenius limit

KW - Hilbert–Kunz multiplicity

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U2 - 10.1016/j.aim.2016.09.020

DO - 10.1016/j.aim.2016.09.020

M3 - Article

AN - SCOPUS:84988963917

VL - 305

SP - 144

EP - 164

JO - Advances in Mathematics

JF - Advances in Mathematics

SN - 0001-8708

ER -