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Invariant rings through categories

Alper, Jarod; de Jong, A.J.


We formulate a notion of "geometric reductivity" in an abstract categorical setting which we refer to as adequacy. The main theorem states that the adequacy condition implies that the ring of invariants is finitely generated. This result applies to the category of modules over a bialgebra, the category of comodules over a bialgebra, and the category of quasi-coherent sheaves on an algebraic stack of finite type over an affine base.

CollectionsANU Research Publications
Date published: 2013
Type: Journal article
Source: Journal of Algebra
DOI: 10.1016/j.jalgebra.2012.11.005


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