Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Perfect correspondences and Chow motives   It is an open conjecture of Orlov that the bounded derived category of
coherent sheaves of a smooth projective variety determines its Chow motive with
rational coefficients. In this master's thesis we introduce a category of
\emph{perfect correspondences}, whose objects are smooth projective varieties
and morphisms $X \to Y$ are perfect complexes on $X \times Y$. We show that
isomorphism in this category is the same as equivalence of derived categories,
and use this to show that the derived category determines the noncommutative
Chow motive (in the sense of Tabuada) and, up to Tate twists, the commutative
Chow motive with rational coefficients. In particular, all additive invariants
like K-theory and Hochschild or cyclic homology depend only on the derived
category.

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The categories of this paper are: atom-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: nucl-ex
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The categories of this paper are: mtrl-th
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The categories of this paper are: comp-gas
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The categories of this paper are: alg-geom
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The categories of this paper are: hep-lat
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The categories of this paper are: adap-org
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The categories of this paper are: ao-sci
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The categories of this paper are: q-fin
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The categories of this paper are: hep-th
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The categories of this paper are: stat
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The categories of this paper are: econ
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The categories of this paper are: cond-mat
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The categories of this paper are: q-bio
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The categories of this paper are: funct-an