Claude Sabbah : Aspects of the irregular Hodge filtration

Posted by Mihnea Popa , part of the Algebraic Geometry Seminar.

At

Feb. 27, 2014, 2 p.m.

In

SEO 636

Abstract

Given a regular function f on a smooth quasi-projective variety U, the de Rham complex of U relative to the twisted differential d + df can be equipped canonically with a filtration (the irregular Hodge filtration) for which the associated hypercohomology spectral sequence degenerates at E_1. A logarithmic version of this de Rham complex (relative to a suitable compactification of U) has been introduced by M. Kontsevich, who showed the independence of the dimension of the corresponding cohomologies with respect to the differential ud +vdf, for u,v arbitrary complex numbers. This leads to bundles on the projective line of the (u:v) variable, on which we construct a natural connection for which the Harder-Narasimhan filtration satisfies the Griffiths transversality property and standard limiting properties at v=0. This is a joint work with Hélène Esnault (Berlin) and Jeng-Daw Yu (Taipei).

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