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SUMMARY:Goren-Oort stratification and Tate cycles on Hilbert modular varie
ties
DTSTART;VALUE=DATE-TIME:20131113T090000Z
DTEND;VALUE=DATE-TIME:20131113T100000Z
DTSTAMP;VALUE=DATE-TIME:20191120T094100Z
UID:indico-event-406@indico.math.cnrs.fr
DESCRIPTION:Let B be a quaternionic algebra over a totally real field F\,
and p be a prime at least 3 unramified in F. We consider a Shimura variety
X associated to B* of level prime to p. A generalization of Deligne-Caray
ol's "modèle étrange" allows us to define an integral model for X. We wi
ll then define a Goren-Oort stratification on the characteristic p fiber o
f X\, and show that each closed Goren-Oort stratum is an iterated P1-fibra
tion over another quaternionic Shimura variety in characteristic p. Now su
ppose that [F:Q] is even and that p is inert in F. An iteration of this co
nstruction gives rise to many algebraic cycles of middle codimension on th
e characteristic p fibre of Hilbert modular varieties of prime-to-p level.
We show that the cohomological classes of these cycles generate a large s
ubspace of the Tate cycles\, which\, in some special cases\, coincides wit
h the prediction of the Tate conjecture for the Hilbert modular variety ov
er finite fields. This is a joint work with Liang Xiao.\n\n Page web du
séminaire\n\nhttps://indico.math.cnrs.fr/event/406/
LOCATION:IHES Centre de conférences Marilyn et James Simons
URL:https://indico.math.cnrs.fr/event/406/
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