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Quasi-unipotent logarithmic Riemann-Hilbert correspondences. (English) Zbl 1082.14024

J. Math. Sci., Tokyo 12, No. 1, 1-66 (2005); erratum ibid. 14, No. 1, 113-116 (2007).
The authors generalize the logarithmic version of the Riemann-Hilbert correspondence defined by K. Kato and C. Nakayama [Kodai Math. J. 22, No. 2, 161–186 (1999; Zbl 0957.14015)] to local systems with quasi-unipotent local monodromies by working a certain Grothendieck topology. They discuss its behavior with respect to direct images and give applications to nearby cycles and the degeneration of relative log Hodge to log de Rham spectral sequences.

MSC:

14F40 de Rham cohomology and algebraic geometry
14F20 Étale and other Grothendieck topologies and (co)homologies
32C38 Sheaves of differential operators and their modules, \(D\)-modules
32G20 Period matrices, variation of Hodge structure; degenerations

Citations:

Zbl 0957.14015
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