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SUMMARY:Dmitrii Pirozhkov (Université de Paris)
DTSTART:20210525T150000Z
DTEND:20210525T160000Z
DTSTAMP:20260423T021606Z
UID:DerSem/27
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/DerSem/27/">
 Stably semiorthogonally indecomposable varieties</a>\nby Dmitrii Pirozhkov
  (Université de Paris) as part of Derived seminar\n\n\nAbstract\nA triang
 ulated category is said to be indecomposable if it admits no nontrivial se
 miorthogonal decompositions. For a derived category of coherent sheaves on
  a variety Y\, we propose a stronger condition\, which implies\, among oth
 er things\, that for any variety X\, any semiorthogonal decomposition of t
 he product X x Y is induced from a decomposition of X. For X = {pt} this i
 mplies the usual indecomposability. We show that varieties with finite Alb
 anese morphism\, e.g.\, curves of positive genus\, are stably semiorthogon
 ally indecomposable in this sense. From this\, we deduce the non-existence
  of phantom subcategories in the product surfaces C x P^1\, where C is a s
 mooth projective curve of positive genus\, and in some other examples as w
 ell.\n
LOCATION:https://researchseminars.org/talk/DerSem/27/
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