Algebraic Geometry Seminar
Dmitri Orlov
Steklov Institute
Uniqueness of enhancements for triangulated categories
Abstract: I am going to talk about triangulated categories in algebra, geometry and
physics, and about differential-graded (DG) enhancements of triangulated
categories. It can be proved that unique DG enhancements exist
for a large class of triangulated categories. This class includes
all derived categories of quasi-coherent sheaves, bounded
derived categories of coherent sheaves, and the category of perfect
complexes on quasi-projective schemes, as well as on a noncommutative
varieties.
This shows that triangulated categories which have a geometric nature
are distinguished among all of triangulated categories, for which
this property does not hold in general.
These results have also applications to the deformation theory of
objects in derived categories, and to homological mirror symmetry.
The talk is based on a joint paper with Valery Lunts.
Wednesday April 13, 2011 at 4:00 PM in SEO 1227