Invariant rings through categories
Algebraic Geometry
2010-11-10 v1 Commutative Algebra
Abstract
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 a finite type algebraic stack over an affine base.
Cite
@article{arxiv.1011.2184,
title = {Invariant rings through categories},
author = {Jarod Alper and A. J. de Jong},
journal= {arXiv preprint arXiv:1011.2184},
year = {2010}
}