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arXiv · 2001.11620

Koszul and local cohomology, and a question of Dutta

Linquan Ma·Anurag K. Singh·Uli Walther
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Abstract

For a local ring $(A,\mathfrak{m})$ of dimension $n$, we study the natural map from the Koszul cohomology module $H^n(\mathfrak{m}; A)$ to the local cohomology module $H^n_\mathfrak{m}(A)$. We prove that the injectivity of this map characterizes the Cohen-Macaulay property of the ring $A$. We also answer a question of Dutta by constructing normal rings $A$ for which this map is zero.

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Linquan Ma, Anurag K. Singh, Uli Walther. 2020-01-31. Koszul and local cohomology, and a question of Dutta. https://arxiv.org/abs/2001.11620

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