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2016 Homotopy theory of mixed Hodge complexes
Joana Cirici, Francisco Guillén
Tohoku Math. J. (2) 68(3): 349-375 (2016). DOI: 10.2748/tmj/1474652264


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.


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Joana Cirici. Francisco Guillén. "Homotopy theory of mixed Hodge complexes." Tohoku Math. J. (2) 68 (3) 349 - 375, 2016.


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

zbMATH: 1359.55013
MathSciNet: MR3550924
Digital Object Identifier: 10.2748/tmj/1474652264

Primary: 55U35
Secondary: 32S35

Keywords: absolute filtration , Cartan-Eilenberg category , décalage , diagram category , filtered derived category , Homotopical algebra , mixed Hodge complex , mixed Hodge theory , weight filtration

Rights: Copyright © 2016 Tohoku University


Vol.68 • No. 3 • 2016
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