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SUMMARY:Topology Seminar: Classical and noncommutative Voevodsky's conject
 ure for cubic fourfolds and Gushel-Mukai fourfolds
DTSTART:20180220T101500
DTEND:20180220T111500
DTSTAMP:20260510T135540Z
UID:89d2ba2da32c13c823b4112a0267549928799fe79d42101cf94c5775
CATEGORIES:Conferences - Seminars
DESCRIPTION:Laura Pertusi (University of Milan)\nIn a seminal paper\, Voev
 odsky introduced the smash-nilpotence equivalence relation on the group of
  algebraic cycles on a smooth projective variety. He also conjectured that
  the nilpotence equivalence corresponds to the classical numerical equival
 ence on cycles. More recently\, Bernardara\, Marcolli and Tabuada defined 
 a noncommutative version of this conjecture for smooth and proper dg categ
 ories. They proved the equivalence between the classical conjecture and th
 eir noncommutative version for the unique enhancement of the derived categ
 ory of perfect complexes on a smooth projective k-scheme.\n\nThe aim of th
 is talk is to prove Voevodsky's conjecture for cubic fourfolds and generic
  Gushel-Mukai fourfolds. Then\, we deduce the noncommutative version of th
 is conjecture for the K3 subcategory appearing in the semiorthogonal decom
 position of the derived category of perfect complexes on a cubic fourfold 
 and on a generic GM fourfold\, introduced by Kuznetsov and Kuznetsov-Perry
 . Finally\, we apply this result to deduce Voevodsky's conjecture for spec
 ial classes of GM fourfolds. This is a joint work with Mattia Ornaghi.
LOCATION:CM 1 113 https://plan.epfl.ch/?room==CM%201%20113
STATUS:CONFIRMED
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