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

Authors :: Hélène Esnault
Marc Levine
Olivier Wittenberg
Department of Mathematics and Computer Science (Freie Universität Berlin)
Freie Universität Berlin
Universität Duisburg-Essen, Fakultät für Mathematik
Centre National de la Recherche Scientifique (CNRS)
Département de Mathématiques et Applications - ENS Paris (DMA)
Centre National de la Recherche Scientifique (CNRS)-École normale supérieure - Paris (ENS Paris)
Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)
École normale supérieure - Paris (ENS Paris)
Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)
Source :: Journal of Algebraic Geometry, Journal of Algebraic Geometry, American Mathematical Society, 2015, 24 (4), pp.693-718. ⟨10.1090/jag/639⟩
Publication Year :: 2015
Publisher :: American Mathematical Society (AMS), 2015.
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 0dim(X)+1). When p=0, such statements also have implications for the possible multiplicities of singular fibers in degenerations of complex projective varieties.<br />Comment: 20 pages; final version

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