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SUMMARY:Matthieu Piquerez - 15h30 - Tropical Hodge theory and the tropical
Hodge conjecture
DTSTART;VALUE=DATE-TIME:20201216T143000Z
DTEND;VALUE=DATE-TIME:20201216T153000Z
DTSTAMP;VALUE=DATE-TIME:20210227T065924Z
UID:indico-event-6420@indico.math.cnrs.fr
DESCRIPTION:Classical Hodge theory explains us that the cohomology of a sm
ooth projective complex variety verifies a lot of nice properties. After a
few reminders about classical Hodge theory and about tropical varieties\,
I will present a tropical analogous of these properties for the cohomolog
y of a tropical variety [arXiv:2007.07826]. This tropical Hodge theory is
strongly linked to combinatorial Hodge theory\, as well as to the limit of
families of complex varieties. I will only detail the latter. This will a
llow me to talk about the tropical Hodge conjecture and to discuss its lin
ks with the classical Hodge conjecture. Finally\, I will present a work in
preparation with O. Amini where we use the tropical Hodge theory to prove
the tropical Hodge conjecture for rationally triangulable tropical variet
ies.\n\nhttps://indico.math.cnrs.fr/event/6420/
LOCATION:
URL:https://indico.math.cnrs.fr/event/6420/
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