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SUMMARY:Relative spherical objects and spherical fibrations - Logvinenko\,
  T (Warwick)
DTSTART:20110407T153000Z
DTEND:20110407T163000Z
UID:TALK30760@talks.cam.ac.uk
CONTACT:Mustapha Amrani
DESCRIPTION:Seidel and Thomas introduced some years ago a notion of a sphe
 rical object in the derived category D(X) of a smooth projective variety X
 . We introduce a relative analogue of this notion by defining what does it
  mean for an object E of the derived category D(Z x X) of a fiber product 
 of two schemes Z and X to be spherical over Z.\nFor objects of D(Z x X) wh
 ich are orthogonal over Z (these are categorical equivalents of a subschem
 e of X fibered over Z) we show an object to be spherical over Z if and onl
 y if it possesses certain cohomological properties similar to those in the
  original definition by Seidel and Thomas. We then interpret this geometri
 cally for the special case where our objects are actual flat subschemes of
  X flatly fibered over Y. This is a joint work with Rina Anno of UChicago.
 "\n\n
LOCATION:Seminar Room 1\, Newton Institute
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