Espaces analytiques sous-algébriques
Espaces de Moisezon relatifs et algébrisation des modifications analytiques.
Essential dimension of moduli of curves and other algebraic stacks
In this paper we consider questions of the following type. Let be a base field and be a field extension. Given a geometric object over a field (e.g. a smooth curve of genus ), what is the least transcendence degree of a field of definition of over the base field ? In other words, how many independent parameters are needed to define ? To study these questions we introduce a notion of essential dimension for an algebraic stack. Using the resulting theory, we give a complete answer to...
Etendues and stacks as bicategories of fractions
Extension of the concept of n-function to categories
Géométrie algébrique de Poisson et déformations
Glatte Morphismen in der affinoiden Geometrie.
Groupes de Chow et K-théorie de variétés sur un corps fini.
Higher Abel-Jacobi maps.
Intégration motivique sur les schémas formels
Nous généralisons la théorie de l’intégration motivique au cadre des schémas formels. Nous définissons et étudions l’anneau booléen des ensembles mesurables, la mesure motivique, l’intégrale motivique et nous démontrons un théorème de changement de variables pour cette intégrale.
La conjecture de Milnor
Local L-factors of motives and regularized determinants.
Logarithmic geometry and algebraic stacks
Matrix factorizations and singularity categories for stacks
We study matrix factorizations of a potential W which is a section of a line bundle on an algebraic stack. We relate the corresponding derived category (the category of D-branes of type B in the Landau-Ginzburg model with potential W) with the singularity category of the zero locus of W generalizing a theorem of Orlov. We use this result to construct push-forward functors for matrix factorizations with relatively proper support.
Moduli for stable marked trees of projective lines.
Motifs des variétés algébriques
Motifs, L-Functions, and the K-Cohomology of Rational Surfaces over Finite Fields.
Motives for modular forms.
Motives, numerical equivalence, and semi-simplicity.
Motivi associati a successioni di coomologia relativa