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- W2890592504 abstract "Let $R$ be a standard graded algebra over a field $k$, with irrelevant maximal ideal $fm$, and $I$ a homogeneous $R$-ideal. We study the asymptotic vanishing behavior of the graded components of the local cohomology modules ${HH{i}{fm}{R/I^n}}_{nin NN}$ for $i<dim R/I$. We show that, when $chara k= 0$, $R/I$ is Cohen-Macaulay, and $I$ is a complete intersection locally on $Spec R setminus{fm}$, the lowest degrees of the modules ${HH{i}{fm}{R/I^n}}_{nin NN}$ are bounded by a linear function whose slope is controlled by the generating degrees of the dual of $I/I^2$. Our result is a direct consequence of a related bound for symmetric powers of locally free modules. If no assumptions are made on the ideal or the field $k$, we show that the complexity of the sequence of lowest degrees is at most polynomial, provided they are finite. Our methods also provide a result on stabilization of maps between local cohomology of consecutive powers of ideals." @default.
- W2890592504 created "2018-09-27" @default.
- W2890592504 creator A5009528753 @default.
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- W2890592504 date "2018-09-07" @default.
- W2890592504 modified "2023-10-03" @default.
- W2890592504 title "On asymptotic vanishing behavior of local cohomology" @default.
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- W2890592504 doi "https://doi.org/10.48550/arxiv.1809.02310" @default.
- W2890592504 hasPublicationYear "2018" @default.
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