Structure de Hodge mixte sur la cohomologie évanescente (Q790892)

Let \(X\to S\) be a proper morphism of an integral \({\mathbb{C}}\)-scheme in a germ of algebraic curve smooth on \({\mathbb{C}}\). A mixed Hodge structure on the vanishing cohomologies is constructed by resolving the vanishing complexes \(R\psi_ X\) and \(R\phi_ X\) by mixed Hodge cohomological complexes. This gives a majoration of the monodromy unipotency level.