Local Cohomology of Modular Invariant Rings

Pub Date : 2024-03-13 DOI:10.1007/s00031-024-09851-6

Kriti Goel, Jack Jeffries, Anurag K. Singh

引用次数: 0

Abstract

For K a field, consider a finite subgroup G of \({\text {GL}}_n(K)\) 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.

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模块不变环的局部同调

对于 K 这个域，考虑 G 的有限子群（{\text {GL}}_n(K)\）及其在多项式环 \(R:=K[x_1,\dots ,x_n]\)上的自然作用。让 \(\mathfrak {n}\) 表示不变式环 \(R^G\)的同质最大理想。我们将研究局部同调模块 \(H^n_{\mathfrak {n}}(R^G)\) 与 \(H^n_{\mathfrak {n}}(R)^G\) 的比较。结果得到了关于 \(H^n_\mathfrak {n}(R^G)\) 的 a-invariant 和 Hilbert 序列的各种结果。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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