Reductivity properties over an affine base
Wilberd van der Kallen
TL;DR
This paper surveys the concepts of power reductivity and geometric reductivity of group schemes over an affine base, emphasizing their roles in invariant theory and the finite generation of invariant subrings.
Contribution
It clarifies the distinctions and relationships between power reductivity and geometric reductivity over non-field bases, providing a comprehensive overview.
Findings
Power reductivity is crucial for finite generation of invariant subrings.
Geometric reductivity is less relevant when the base is not a field.
The paper connects reductivity properties with invariant theory over affine bases.
Abstract
When the base ring is not a field, power reductivity of a group scheme is a basic notion, intimately tied with finite generation of subrings of invariants. Geometric reductivity is weaker and less pertinent in this context. We give a survey of these properties and their connections.
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