Arithmetic Invariant Theory of Reductive Groups
Yidi Wang
TL;DR
This paper explores the properties of linearly reductive groups over rings and investigates the Cohen-Macaulay property of their invariant rings, providing new insights into reductivity notions over certain regular rings.
Contribution
It introduces the concept of linearly reductive groups over rings and analyzes the Cohen-Macaulay property of invariant rings, also comparing reductivity notions over regular rings of Krull dimension two.
Findings
Characterization of linearly reductive groups over rings
Conditions for Cohen-Macaulay property of invariant rings
Equivalence of reductivity notions over specific regular rings
Abstract
In this manuscript, we define the notion of linearly reductive groups over commutative unital rings and study the Cohen-Macaulay property of the ring of invariants under rational actions of a linearly reductive group. Moreover, we study the equivalence of different notions of reductivity over regular rings of Krull dimension two by studying these properties locally.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Advanced Algebra and Geometry · Algebraic Geometry and Number Theory