The Regular property of Invariant Rings over Regular Domains

2025/11/16 by Jaiswal, Shubham, Puthenpurakal, Tony J.
#13H05 #Commutative Algebra (math.AC) #FOS: Mathematics #Primary 13A50

paper · doi:10.48550/arxiv.2511.12569

Abstract

The main result of this paper is a generalization of the theorem of Chevalley-Shephard-Todd to the rings of invariants of pseudo-reflection groups over regular domains. More precisely, let A be a regular domain and let K be its field of fractions. Let G⊆ GL_n(A) be a finite group. Let G act linearly on A[X₁,X₂,…, X_n] (fixing A). Assume that |G| is invertible in A. We prove that if G⊆ GL_n(K) is generated by psuedo-reflections then (A[X₁,X₂,…, X_n])^G is regular.

Citations

• On two dimensional mixed characteristic rings of finite Cohen Macaulay type

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