On a conjecture of Kashiwara

Details On a conjecture of Kashiwara On a conjecture of Kashiwara

2001-08-07

arxiv.org/abs/math/0108050v3

Mathematics

Algebraic Geometry

16 pages, Latex; added references to works by Simpson and Sabbah

Scientific paper

Kashiwara conjectured that the hard Lefshetz theorem and the semisimplicity theorem hold for any semisimple perverse sheaf M on a variety over a field of characteristic 0. He also conjectured that if you apply to such M the nearby cycle functor corresponding to some function then the successive quotients of the monodromy filtration are semisimple. We prove that these conjectures would follow from de Jong's conjecture on representations modulo l of the arithmetic fundamental group of a variety over a finite field.

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