Derived categories of coherent sheaves and motives
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Fri, 27/05/2011 12:00 |
Shane Kelly (Universite Paris 13) |
Junior Geometry and Topology Seminar  |
SR1 |
| The derived category of a variety has (relatively) recently come into play as an invariant of the variety, useful as a tool for classification. As the derived category contains cohomological information about the variety, it is perhaps a natural question to ask how close the derived category is to the motive of a variety. We will begin by briefly recalling Grothendieck's category of Chow motives of smooth projective varieties, recall the definition of Fourier-Mukai transforms, and state some theorems and examples. We will then discuss some conjectures of Orlov http://arxiv.org/abs/math/0512620, the most general of which is: does an equivalence of derived categories imply an isomorphism of motives? | |||