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arXiv · 1207.1883

Index of varieties over Henselian fields and Euler characteristic of coherent sheaves

Hélène Esnault·Marc Levine·Olivier Wittenberg
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Abstract

Let X be a smooth proper variety over the quotient field of a Henselian discrete valuation ring with algebraically closed residue field of characteristic p. We show that for any coherent sheaf E on X, the index of X divides the Euler-Poincar\'e characteristic \chi(X,E) if p=0 or p>dim(X)+1. If 0 dim(X)+1). When p=0, such statements also have implications for the possible multiplicities of singular fibers in degenerations of complex projective varieties.

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Hélène Esnault, Marc Levine, Olivier Wittenberg. 2012-07-08. Index of varieties over Henselian fields and Euler characteristic of coherent sheaves. https://doi.org/10.1090/jag/639

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