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On the highest Lyubeznik number of a local ring

Wenliang Zhang
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Abstract

Let $A$ be a $d$-dimensional local ring containing a field. We will prove that the highest Lyubeznik number $λ_{d,d}(A)$ (defined in \cite{l1}) is equal to the number of connected components of the Hochster-Huneke graph (defined in \cite{hh}) associated to $B$, where $B=\hat{\hat{A}^{sh}}$ is the completion of the strict Henselization of the completion of $A$. This was proven by Lyubeznik in characteristic $p>0$. Our statement and proof are characteristic-free.

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Wenliang Zhang. 2006-02-25. On the highest Lyubeznik number of a local ring. https://arxiv.org/abs/math/0602566

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