Invariant rings through categories

Jarod Alper; A. J. de Jong

doi:10.1016/j.jalgebra.2012.11.005

Invariant rings through categories

Jarod Alper^*, A. J. de Jong

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

3 Citations (Scopus)

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 an algebraic stack of finite type over an affine base.

Original language	English
Pages (from-to)	235-257
Number of pages	23
Journal	Journal of Algebra
Volume	375
DOIs	https://doi.org/10.1016/j.jalgebra.2012.11.005
Publication status	Published - 1 Feb 2013

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10.1016/j.jalgebra.2012.11.005

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title = "Invariant rings through categories",

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 an algebraic stack of finite type over an affine base.",

keywords = "Algebraic geometry, Algebraic stacks, Categories, Hopf algebras, Invariant theory",

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AU - Alper, Jarod

AU - de Jong, A. J.

PY - 2013/2/1

Y1 - 2013/2/1

N2 - 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.

AB - 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.

KW - Algebraic geometry

KW - Algebraic stacks

KW - Categories

KW - Hopf algebras

KW - Invariant theory

UR - http://www.scopus.com/inward/record.url?scp=84870494750&partnerID=8YFLogxK

U2 - 10.1016/j.jalgebra.2012.11.005

DO - 10.1016/j.jalgebra.2012.11.005

M3 - Article

SN - 0021-8693

VL - 375

SP - 235

EP - 257

JO - Journal of Algebra

JF - Journal of Algebra

ER -

Invariant rings through categories

Abstract

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