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arXiv · 2404.10592

Module schemes in invariant theory

Holger Brenner
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Abstract

Let G be a finite group acting linearly on the polynomial ring with invariant ring R. If the action is small, then a classical result of Auslander gives in dimension two a correspondence between linear representations of G and maximal Cohen-Macaulay R-modules. We establish a correspondence for all linear actions between representations and objects over the invariant ring by looking at quotient module schemes (up to modification) instead of the modules of covariants.

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Holger Brenner. 2024-04-16. Module schemes in invariant theory. https://arxiv.org/abs/2404.10592

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