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On the highest Lyubeznik number of a local ring

Published online by Cambridge University Press:  19 January 2007

Wenliang Zhang
Wenliang Zhang
Affiliation:
Department of Mathematics, University of Minnesota, Minneapolis, MN 55455, USAwlzhang@math.umn.edu
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Abstract

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Let $A$ be a $d$-dimensional local ring containing a field. We will prove that the highest Lyubeznik number $\lambda_{d,d}(A)$ is equal to the number of connected components of the Hochster–Huneke graph associated to $B$, where $B=\widehat{\hat{A}^{\rm sh}}$ 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.

Keywords

local cohomologyLyubeznik numbers13D4513H9914B15
Type
Research Article
Information
Compositio Mathematica , Volume 143 , Issue 1 , January 2007 , pp. 82 - 88
Copyright
Foundation Compositio Mathematica 2007