Exponential Hodge theory (I)


Claude Sabbah

13:30:00 - 14:20:00

101 , Mathematics Research Center Building (ori. New Math. Bldg.)

Given a regular function f on a smooth quasi-projective variety U, J.-D. Yu (Taipei) has canonically equipped the de Rham complex of U relative to the twisted differential d+ df with a filtration (the irregular Hodge filtration) for which the associated hypercohomology spectral sequence degenerates at E_1. M. Kontsevich has introduced a logarithmic version of this de Rham complex (relative to a suitable compactification of U) and has shown the independence of the dimension of the corresponding cohomologies with respect to the differential ud + vdf, for arbitrary complex numbers u,v. This leads to bundles on the projective line of the (u:v) variable, on which one constructs a natural connection for which the Harder-Narasimhan filtration satisfies the Griffiths transversality property and standard limiting properties at v=0. This lecture surveys joint works with H. Esnault and J.-D. Yu, and works by Katzarkov-Kontsevich-Pantev and by T. Mochizuki.