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Direct image of logarithmic complexes and infinitesimal invariants of cycles. (English) Zbl 1125.14007
Nagel, Jan (ed.) et al., Algebraic cycles and motives. Volume 2. Selected papers of the EAGER conference, Leiden, Netherlands, August 30–September 3, 2004 on the occasion of the 75th birthday of Professor J. P. Murre. Cambridge: Cambridge University Press (ISBN 978-0-521-70175-4/pbk). London Mathematical Society Lecture Note Series 344, 304-318 (2007).
It is shown that the direct image of the filtered logarithmic de Rham complex is a direct sum of filtered logarithmic complexes with coefficients in variations of Hodge structures. Applications of this result to the total infinitesimal invariant of a cycle in a higher Chow group and to a vanishing result similar to Kodaira-Nakano Theorem are included.
For the entire collection see [Zbl 1113.14002].

14F40 de Rham cohomology and algebraic geometry
14C30 Transcendental methods, Hodge theory (algebro-geometric aspects)
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