The Regular property of Invariant Rings over Regular Domains
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866912973350502400 |
|---|---|
| author | Jaiswal, Shubham Puthenpurakal, Tony J. |
| author_facet | Jaiswal, Shubham Puthenpurakal, Tony J. |
| contents | 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 $G\subseteq GL_n(A)$ be a finite group. Let $G$ act linearly on $A[X_1,X_2,\dots, X_n]$ (fixing $A$). Assume that $|G|$ is invertible in $A$. We prove that $G\subseteq GL_n(K)$ is generated by pseudo-reflections if and only if $(A[X_1,X_2,\dots, X_n])^G$ is regular. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_12569 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The Regular property of Invariant Rings over Regular Domains Jaiswal, Shubham Puthenpurakal, Tony J. Commutative Algebra Primary 13A50, 13H05 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 $G\subseteq GL_n(A)$ be a finite group. Let $G$ act linearly on $A[X_1,X_2,\dots, X_n]$ (fixing $A$). Assume that $|G|$ is invertible in $A$. We prove that $G\subseteq GL_n(K)$ is generated by pseudo-reflections if and only if $(A[X_1,X_2,\dots, X_n])^G$ is regular. |
| title | The Regular property of Invariant Rings over Regular Domains |
| topic | Commutative Algebra Primary 13A50, 13H05 |
| url | https://arxiv.org/abs/2511.12569 |