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
SN - 0001-8708
VL - 305
SP - 144
EP - 164
JO - Advances in Mathematics
JF - Advances in Mathematics
ER -