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1 results

  • On the highest Lyubeznik number of a local ring

  • Wenliang Zhang
  • Journal:
    Compositio Mathematica / Volume 143 / Issue 1 / January 2007
    Published online by Cambridge University Press:
    19 January 2007, pp. 82-88
    Print publication:
    January 2007
    • Article
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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.