From exceptional collections to motivic decompositions, by Matilde Marcolli and Goncalo Tabuada

In this article we prove that the Chow motive of every smooth and proper Deligne-Mumford stack, whose bounded derived category of coherent schemes admits a full exceptional collection, decomposes into a direct sum of tensor powers of the Lefschetz motive. Examples include projective spaces, quadrics, toric varieties, homogeneous spaces, Fano threefolds, and moduli spaces. As an application we obtain explicit obstructions for the existence of full exceptional collections and a simplification of Dubrovin's conjecture.

Matilde Marcolli <>
Goncalo Tabuada <>