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Hodge realizations of 1-motives and the derived Albanese

Published online by Cambridge University Press:  31 January 2012

Vadim Vologodsky
Vadim Vologodsky*
Affiliation:
Department of Mathematics, University of Oregon, Eugene, OR, 97403, USAvvologod@uoregon.edu
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Abstract

We prove that the embedding of the derived category of 1-motives up to isogeny into the triangulated category of effective Voevodsky motives, as well as its left adjoint functor LAlbℚ, commute with the Hodge realization. This result yields a new proof of the rational form of Deligne's conjecture on 1-motives.

Keywords

Algebraic cyclesVoevodsky motivesHodge theory

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Type
Research Article
Information
Journal of K-Theory , Volume 10 , Issue 2 , October 2012 , pp. 371 - 412
Copyright
Copyright © ISOPP 2011

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