On the Highest Lyubeznik Number of a Local Ring

نویسنده

WENLIANG ZHANG

چکیده

Let A be a d-dimensional local ring containing a field. We will prove that the highest Lyubeznik number λd,d(A) (defined in [5]) is equal to the number of connected components of the Hochster-Huneke graph (defined in [2]) associated to B, where B = ̂̂ Ash 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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