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Tohoku Mathematical Journal
SECOND SERIES VOL. 68, NO. 3
|Tohoku Math. J.|
68 (2016), 349-375
HOMOTOPY THEORY OF MIXED HODGE COMPLEXES
In memoriam Alexander Grothendieck
Joana Cirici and Francisco Guillén
(Received February 17, 2014, revised November 25, 2014)
We show that the category of mixed Hodge complexes admits a Cartan-Eilenberg structure, a notion introduced by Guillén-Navarro-Pascual-Roig leading to a good calculation of the homotopy category in terms of (co)fibrant objects. Using Deligne's décalage, we show that the homotopy categories associated with the two notions of mixed Hodge complex introduced by Deligne and Beilinson respectively, are equivalent. The results provide a conceptual framework from which Beilinson's and Carlson's results on mixed Hodge complexes and extensions of mixed Hodge structures follow easily.
Mathematics Subject Classification.
Primary 55U35; Secondary 32S35.
Key words and phrases.
Mixed Hodge theory, homotopical algebra, mixed Hodge complex, filtered derived category, weight filtration, absolute filtration, diagram category, Cartan-Eilenberg category, décalage.
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