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arXiv · 1509.04374

F-rationality of the ring of modular invariants

Mitsuyasu Hashimoto
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Abstract

Using the description of the Frobenius limit of modules over the ring of invariants under an action of a finite group on a polynomial ring over a field of characteristic $p>0$ developed by Symonds and the author, we give a characterization of the ring of invariants with a positive dual $F$-signature. Combining this result and Kemper's result on depths of the ring of invariants under an action of a permutation group, we give an example of an $F$-rational, but non-$F$-regular ring of invariants under the action of a finite group.

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Mitsuyasu Hashimoto. 2015-09-15. F-rationality of the ring of modular invariants. https://arxiv.org/abs/1509.04374

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