Summary: INVARIANT RINGS THROUGH CATEGORIES
JAROD ALPER AND A. J. DE JONG
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 gen-
erated. 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.
Contents
1. Introduction 1
2. Setup 2
3. Axioms 3
4. Direct summands 4
5. Commutativity 5
6. Direct products 5
7. Symmetric products 6
8. Ring objects 6
9. Commutative ring objects and modules 8
10. Finiteness conditions 9
11. Adequacy 10

Source: Alper, Jarod - Department of Mathematics, Columbia University

Collections: Mathematics