Tohoku Mathematical Journal

Homotopy theory of mixed Hodge complexes

Joana Cirici and Francisco Guillén

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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.

Article information

Tohoku Math. J. (2) Volume 68, Number 3 (2016), 349-375.

Received: 17 February 2014
Revised: 25 November 2014
First available in Project Euclid: 23 September 2016

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 55U35: Abstract and axiomatic homotopy theory
Secondary: 32S35: Mixed Hodge theory of singular varieties [See also 14C30, 14D07]

Mixed Hodge theory homotopical algebra mixed Hodge complex filtered derived category weight filtration absolute filtration diagram category Cartan-Eilenberg category décalage


Cirici, Joana; Guillén, Francisco. Homotopy theory of mixed Hodge complexes. Tohoku Math. J. (2) 68 (2016), no. 3, 349--375. doi:10.2748/tmj/1474652264.

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