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SUMMARY:Parity of Betti numbers in étale cohomology
DTSTART;VALUE=DATE-TIME:20140521T083000Z
DTEND;VALUE=DATE-TIME:20140521T093000Z
DTSTAMP;VALUE=DATE-TIME:20210731T224613Z
UID:indico-event-359@indico.math.cnrs.fr
DESCRIPTION:By Hodge symmetry\, the Betti numbers of a complex projective
smooth variety in odd degrees are even. When the base field has characteri
stic p\, Deligne proved the hard Lefschetz theorem in étale cohomology\,
and the parity result follows from this. Suh has generalized this to prope
r smooth varieties in characteristic p\, using crystalline cohomology. The
purity of intersection cohomology group of proper varieties suggests that
the same parity property should hold for these groups in characteristic p
. We proved this by investigating the symmetry in the categorical level. I
n particular\, we reproved Suh's result\, using merely étale cohomology.
Some related results will be discussed. This is joint work with Weizhe Zhe
ng.\n\nPage web du séminaire\n\nhttps://indico.math.cnrs.fr/event/359/
LOCATION:IHES Centre de conférences Marilyn et James Simons
URL:https://indico.math.cnrs.fr/event/359/
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