TY - JOUR
T1 - E1-degeneration of the irregular Hodge filtration
AU - Esnault, Hélène
AU - Sabbah, Claude
AU - Yu, Jeng Daw
AU - Saito, Morihiko
N1 - Publisher Copyright:
© De Gruyter 2017.
PY - 2017/8/1
Y1 - 2017/8/1
N2 - For a regular function f on a smooth complex quasi-projective variety, J.-D. Yu introduced in [35] a filtration (the irregular Hodge filtration) on the de Rham complex with twisted differential d C df , extending a definition of Deligne in the case of curves. In this article, we show the degeneration at E1 of the spectral sequence attached to the irregular Hodge filtration, by using the method of [26].We also make explicit the relation with a complex introduced by M. Kontsevich and give details on his proof of the corresponding E1-degeneration, by reduction to characteristic p, when the pole divisor of the function is reduced with normal crossings. In Appendix E, M. Saito gives a different proof of the E1-degeneration.
AB - For a regular function f on a smooth complex quasi-projective variety, J.-D. Yu introduced in [35] a filtration (the irregular Hodge filtration) on the de Rham complex with twisted differential d C df , extending a definition of Deligne in the case of curves. In this article, we show the degeneration at E1 of the spectral sequence attached to the irregular Hodge filtration, by using the method of [26].We also make explicit the relation with a complex introduced by M. Kontsevich and give details on his proof of the corresponding E1-degeneration, by reduction to characteristic p, when the pole divisor of the function is reduced with normal crossings. In Appendix E, M. Saito gives a different proof of the E1-degeneration.
U2 - 10.1515/crelle-2014-0118
DO - 10.1515/crelle-2014-0118
M3 - Article
AN - SCOPUS:85029228606
SN - 0075-4102
VL - 2017
SP - 171
EP - 227
JO - Journal fur die Reine und Angewandte Mathematik
JF - Journal fur die Reine und Angewandte Mathematik
IS - 729
ER -