Invariants de Hasse-Witt des réductions de certaines variétés symplectiques irréductibles

Details Invariants de Hasse-Witt des réductions de certaines variétés symplectiques irréductibles Invariants de Hasse-Witt des réductions de certaines variétés symplectiques irréductibles

2010-01-18

arxiv.org/abs/1001.2929v2

Mathematics

Algebraic Geometry

15 pages, french. D. Huybrechts pointed out to me that Tate's conjecture was already known to be true for hyperk\"ahler manifo

Scientific paper

Let X be an irreducible symplectic variety defined over a number field K.
Assume either that X has Picard number at least two or that X has even second
Betti number. We prove that there exist a finite algebraic field extension L/K
and a density 1 set S of non-archimedean places of L such that the reduction of
X at any place in S has nonzero Hasse-Witt invariant.

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