Local cohomology of modular invariant rings
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866911795252297728 |
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| author | Goel, Kriti Jeffries, Jack Singh, Anurag K. |
| author_facet | Goel, Kriti Jeffries, Jack Singh, Anurag K. |
| contents | For $K$ a field, consider a finite subgroup $G$ of $\operatorname{GL}_n(K)$ with its natural action on the polynomial ring $R:=K[x_1,\dots,x_n]$. Let $\mathfrak{n}$ denote the homogeneous maximal ideal of the ring of invariants $R^G$. We study how the local cohomology module $H^n_{\mathfrak{n}}(R^G)$ compares with $H^n_{\mathfrak{n}}(R)^G$. Various results on the $a$-invariant and on the Hilbert series of $H^n_\mathfrak{n}(R^G)$ are obtained as a consequence. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2306_14279 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Local cohomology of modular invariant rings Goel, Kriti Jeffries, Jack Singh, Anurag K. Commutative Algebra 13A50 (Primary), 13D45, 13B05 (Secondary) For $K$ a field, consider a finite subgroup $G$ of $\operatorname{GL}_n(K)$ with its natural action on the polynomial ring $R:=K[x_1,\dots,x_n]$. Let $\mathfrak{n}$ denote the homogeneous maximal ideal of the ring of invariants $R^G$. We study how the local cohomology module $H^n_{\mathfrak{n}}(R^G)$ compares with $H^n_{\mathfrak{n}}(R)^G$. Various results on the $a$-invariant and on the Hilbert series of $H^n_\mathfrak{n}(R^G)$ are obtained as a consequence. |
| title | Local cohomology of modular invariant rings |
| topic | Commutative Algebra 13A50 (Primary), 13D45, 13B05 (Secondary) |
| url | https://arxiv.org/abs/2306.14279 |