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• W2056501208 abstract "Making use of noncommutative motives we relate exceptional collections (and more generally semi-orthogonal decompositions) to motivic decompositions. On one hand we prove that the Chow motive M(X) of every smooth proper Deligne-Mumford stack X, whose bounded derived category D(X) 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. On the other hand we prove that if M(X) decomposes into a direct sum of tensor powers of the Lefschetz motive and moreover D(X) admits a semi-orthogonal decomposition, then the noncommutative motive of each one of the pieces of the semi-orthogonal decomposition is a direct sum of the tensor unit. As an application we obtain a simplification of Dubrovin's conjecture." @default.
• W2056501208 created "2016-06-24" @default.
• W2056501208 creator A5007011418 @default.
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• W2056501208 date "2012-02-28" @default.
• W2056501208 modified "2023-09-27" @default.
• W2056501208 title "From exceptional collections to motivic decompositions via noncommutative motives" @default.
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