Abstract
We continue to study the more formal aspects of Hodge theory, this time for the case of mixed Hodge structures. In §3.1 the basic definitions are given; the Deligne splittings are introduced which make it possible to prove strictness of morphisms of mixed Hodge structures and to show that the category of mixed Hodge structures is abelian. The complexes which come up in constructions for mixed Hodge structures have two filtrations and any one of these defines a priori different natural filtrations on the terms of the spectral sequence for the other filtration.We compare these in §3.2. This study reveals (§3.3) that certain abstract properties built in the definition of a mixed Hodge complex of sheaves guarantee that their hypercohomology groups carry a mixed Hodge structure.
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© 2008 Springer-Verlag Berlin Heidelberg
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(2008). Abstract Aspects of Mixed Hodge Structures. In: Mixed Hodge Structures. Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics, vol 52. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-77017-6_4
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DOI: https://doi.org/10.1007/978-3-540-77017-6_4
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-77015-2
Online ISBN: 978-3-540-77017-6
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