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Derived equivalent threefolds, algebraic representatives, and the coniveau filtration

Published online by Cambridge University Press:  08 May 2018

JEFFREY D. ACHTER ,
SEBASTIAN CASALAINA-MARTIN  and
CHARLES VIAL
JEFFREY D. ACHTER
Affiliation:
Colorado State University, Department of Mathematics, Fort Collins, CO 80523, U.S.A.
SEBASTIAN CASALAINA-MARTIN
Affiliation:
University of Colorado, Department of Mathematics, Boulder, CO 80309, U.S.A.
CHARLES VIAL
Affiliation:
Universität Bielefeld, Fakultät für Mathematik, Bielefeld 33501, Germany.
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Abstract

A conjecture of Orlov predicts that derived equivalent smooth projective varieties over a field have isomorphic Chow motives. The conjecture is known for curves, and was recently observed for surfaces by Huybrechts. In this paper we focus on threefolds over perfect fields, and unconditionally secure results, which are implied by Orlov's conjecture, concerning the geometric coniveau filtration, and abelian varieties attached to smooth projective varieties.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 167 , Issue 1 , July 2019 , pp. 123 - 131
Copyright
Copyright © Cambridge Philosophical Society 2018 

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References

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