Modifications et cycles évanescents sur une base de dimension supérieure à un

Details Modifications et cycles évanescents sur une base de dimension supérieure à un Modifications et cycles évanescents sur une base de dimension supérieure à un

2005-07-22

arxiv.org/abs/math/0507475v1

International Mathematics Research Notices 2006 (2006) Article ID 25315, 38 pages

Mathematics

Algebraic Geometry

In French. Submitted to IMRN

Scientific paper

10.1155/IMRN/2006/25315

For a given morphism of schemes f:X->S, a sheaf F on X, a geometric point x on X, and s=f(x), the morphism f\_x : X(x) -> S(s) between the strict henselizations doesn't necessarily behave (with respect to F) like a proper morphism. However, we know it is so (assuming constructibility of F etc.) if S is the spectrum of a dvr (P. Deligne, SGA 4 1/2, [Th. finitude]). In this article, we prove it becomes so after an appropriate modification of the base S. The main ingredient is a theorem by A.J. de Jong on plurinodal fibrations. An application of this formalism to Lefschetz pencils is given.

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