On Lyubeznik’s Invariants and Endomorphisms of Local Cohomology Modules
نویسنده
چکیده
Let (R,m) denote an n-dimensional Gorenstein ring. For an ideal I ⊂ R of height c we are interested in the endomorphism ring B = HomR(H c I (R),H c I (R)). It turns out that B is a commutative ring. In the case of (R, m) a regular local ring containing a field B is a Cohen-Macaulay ring. Its properties are related to the highest Lyubeznik number l = dimk Ext d R(k, H c I (R)). In particular R ≃ B if and only if l = 1. Moreover, we show that the natural homomorphism ExtdR(k, H c I (R)) → k is non-zero.
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