Higher de Rham-Witt complexes of supersingular K3 surfaces
Higher solutions of hypergeometric systems and Dwork cohomology
Hodge metrics and the curvature of higher direct images
Using the harmonic theory developed by Takegoshi for representation of relative cohomology and the framework of computation of curvature of direct image bundles by Berndtsson, we prove that the higher direct images by a smooth morphism of the relative canonical bundle twisted by a semi-positive vector bundle are locally free and semi-positively curved, when endowed with a suitable Hodge type metric.
Holomorphe Differentialformen auf algebraischen Varietäten mit Singularitäten I.
Holomorphic one-forms on varieties of general type
Holonomie sans structure de Frobenius et critères d’holonomie
Ce travail s’inscrit dans le cadre de la théorie des -modules arithmétiques de Berthelot. Nous définissons la notion de -modules arithmétiques holonomes. Lorsque les modules sont munis d’une structure de Frobenius, nous retrouvons la définition d’holonomie de Berthelot. Nous vérifions que l’inégalité de Bernstein et le critère homologique d’holonomie de Virrion restent valables sans l’hypothèse d’une structure de Frobenius. Nous établissons qu’un -module surcohérent (sans structure de Frobenius)...
Homology for irregular connections
Homology with values in a connection with possibly irregular singular points on an algebraic curve is defined, generalizing homology with values in the underlying local system for a connection with regular singular points. Integration defines a perfect pairing between de Rham cohomology with values in the connection and homology with values in the dual connection.
How to calculate the slopes of a -module