Derived categories, noncommutative motives and commutative theorems

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• Marcello Bernardara (Toulouse)
• Wednesday 28 May 2014, 14:15-15:15
• MR 13, CMS.

If you have a question about this talk, please contact Dr. J Ross.

In this talk, I will present results obtained with G.Tabuada and, partially, M.Marcolli. Given a smooth projective variety, one can consider the dg-category perf(X) and the associated non-commutative motive NC(X). A bridge between non-commutative and commutative motives allows one to obtain “commutative” invariants such as intermediate Jacobians and Chow groups from the study of semiorthogonal decompositions of Perf(X). Examples of applications are a proof of a conjecture on Chow groups of some intersections of quadrics and a non-commutative formulation of Voevodsky’s smash-nilpotence conjecture.

This talk is part of the Algebraic Geometry Seminar series.

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