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SUMMARY:Grassmannians and Period Mappings in Derived Algebraic Geometry - 
 Carmelo Di Natale (Cambridge)
DTSTART:20150123T150000Z
DTEND:20150123T160000Z
UID:TALK57597@talks.cam.ac.uk
CONTACT:Joe Waldron
DESCRIPTION:The goal of this talk is to explain how to extend Grassmannian
 s to the world of derived stacks\, i.e. how to construct a satisfying deri
 ved enhancement of Grassmannian varieties. I will begin by discussing some
  background about derived geometric stacks and in particular I will focus 
 on Artin-Lurie-Pridham representability theorem\, which provides us with a
  "computational" criterion to check whether a simplicial presheaf of deriv
 ed algebras is a derived geometric stack. Then I will use such a result in
  order to study derived moduli of perfect complexes and filtered perfect c
 omplexes over a base scheme\; finally the derived Grassmannian will arise 
 as some suitable homotopy limit of such stacks. Time permitting I will end
  by sketching how to use this derived version of the Grassmannian to obtai
 n a derived version of Griffiths' period mapping.
LOCATION:MR13
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