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SUMMARY:The six functor formalism for perverse Nori motives
DTSTART:20231207T130000Z
DTEND:20231207T140000Z
DTSTAMP:20241113T083200Z
UID:indico-event-10909@indico.math.cnrs.fr
DESCRIPTION:Speakers: Luca Terenzi\n\nLet $k$ be a subfield of the complex
numbers. After Deligne\, thesingular cohomology groups with rational coef
ficients ofquasi-projective $k$-varieties are more than just $\\Q$-vector
spaces\,since they carry a canonical $\\Q$-mixed Hodge structure\; all lin
ear mapsbetween cohomology groups "coming from geometry" are automatically
compatible with this additional structure.The theory of Nori motives provi
des a $\\Q$-linear abelian category ofcoefficients which further refines t
he category of $\\Q$-mixed Hodgestructures: in fact\, it is designed to ha
ve the finest possiblestructure that singular cohomology groups of $k$-var
ieties can possiblycarry. Conjecturally\, Nori's category should be the co
rrect abeliancategory of mixed motives over $k$ envisioned by Grothendieck
\,Beilinson\, Deligne and others\; however\, proving this seems to be tota
llyout of reach at present.As conjectured by Beilinson\, the theory of Mix
ed Motives should admit anenhancement to a theory of Mixed Motivic Sheaves
enjoying a complete sixfunctor formalism. In the last decade there have b
een several attemptsat extending Nori's original theory to a theory of "No
ri motivicsheaves"\, the hardest problem being precisely the construction
of thesix functors.After reviewing Nori's original theory in some detail\,
I will presentthe theory of perverse Nori motives recently introduced by
Ivorra andMorel. A complete six functor formalism is now available in this
setting\, by work of Ivorra--Morel and of myself\; the final goal of mytal
k is to sketch the main ideas behind this construction.\n\nhttps://indico.
math.cnrs.fr/event/10909/
URL:https://indico.math.cnrs.fr/event/10909/
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