The asymptotic behavior of Frobenius direct images of rings of invariants
| Autor: | Mitsuyasu Hashimoto, Peter Symonds |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2017 |
| Předmět: |
Pure mathematics
General Mathematics Polynomial ring Hilbert–Kunz multiplicity Commutative Algebra (math.AC) 01 natural sciences symbols.namesake 0103 physical sciences Frobenius algebra FOS: Mathematics Representation Theory (math.RT) 0101 mathematics Frobenius group Frobenius solution to the hypergeometric equation Mathematics Frobenius theorem (real division algebras) Discrete mathematics Finite group Primary 13A50 13A35 Frobenius limit Mathematics::Commutative Algebra 010102 general mathematics Group algebra Mathematics - Commutative Algebra F-signature symbols Grothendieck group Frobenius direct image 010307 mathematical physics Mathematics - Representation Theory |
| Zdroj: | Hashimoto, M & Symonds, P 2016, ' The Asymptotic Behavior of Frobenius Direct Images of Rings of Invariants ', Advances in Mathematics, vol. 305, no. 0, pp. 144-164 . https://doi.org/10.1016/j.aim.2016.09.020 |
| ISSN: | 0001-8708 |
| Popis: | 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. 25 pages |
| Databáze: | OpenAIRE |
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