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Tame loci of certain local cohomology modules. (English) Zbl 1237.13036

Summary: Let \(M\) be a finitely generated graded module over a Noetherian homogeneous ring \(R = \bigoplus_{n \in \mathbb{N}_0}R_n\). For each \(i \in \mathbb{N}_0\) let \(H^i_{R_{+}}(M)\) denote the \(i\)-th local cohomology module of \(M\) with respect to the irrelevant ideal \(R_+ = \bigoplus_{n > 0} R_n\) of \(R\), furnished with its natural grading. We study the tame loci \(\mathfrak t^i(M)^{\leq 3}\) at level \(i \in \mathbb{N}_0\) in codimension \(\leq 3\) of \(M\), that is the sets of all primes \(\mathfrak p_0 \subset R_0\) of height \(\leq 3\) such that the graded \(R_{\mathfrak p_0}\)-modules \(H^i_{R_{+}}(M)_{\mathfrak p_0}\) are tame.

MSC:

13D45 Local cohomology and commutative rings
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