Arithmetic Invariant Theory of Reductive Groups

2022/12/25 by Wang, Yidi
#13A50 #14L30 #20G35 #Commutative Algebra (math.AC) #FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2212.12863

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.

Related

• Arithmetic invariant theory II
• Versal Family of Reductive Groups
• Linear algebraic groups with good reduction
• When are the natural embeddings of classical invariant rings pure?
• On Cohen-Macaulay rings of invariants