-homotopy theory of schemes
A fundamental domain for the Fermat curves and their quotients.
A note on Zariski pairs
A rigidity property of class VIIo surface fundamental groups.
Algebraic and symplectic Gromov-Witten invariants coincide
For a complex projective manifold Gromov-Witten invariants can be constructed either algebraically or symplectically. Using the versions of Gromov-Witten theory by Behrend and Fantechi on the algebraic side and by the author on the symplectic side, we prove that both points of view are equivalent
Algebraic tubular neighbourhoods II.
Altérations et groupe fondamental premier à
Nous démontrons divers résultats sur le plus grand quotient du groupe fondamental étale premier aux caractéristiques, parmi lesquels la formule de Künneth et l’invariance par changement de corps séparablement clos pour les schémas de type fini sur un corps. Ces énoncés sont déduits de faits généraux sur les images directes de champs, une fois spécialisés au cas des torseurs sous un groupe constant fini d’ordre inversible sur la base. Des résultats analogues pour le groupe fondamental modéré sont...
Base change functors in the -stable homotopy category.
Brown-Peterson spectra in stable -homotopy theory
Calculating limits and colimits in pro-categories
We present some constructions of limits and colimits in pro-categories. These are critical tools in several applications. In particular, certain technical arguments concerning strict pro-maps are essential for a theorem about étale homotopy types. We also correct some mistakes in the literature on this topic.
Comparison between the fundamental group scheme of a relative scheme and that of its generic fiber
We show that the natural morphism between the fundamental group scheme of the generic fiber of a scheme over a connected Dedekind scheme and the generic fiber of the fundamental group scheme of is always faithfully flat. As an application we give a necessary and sufficient condition for a finite, dominated pointed -torsor over to be extended over . We finally provide examples where is an isomorphism.
Complex local systems and morphisms of varieties
Co-rank and Betti number of a group
For a finitely generated group, we study the relations between its rank, the maximal rank of its free quotient, called co-rank (inner rank, cut number), and the maximal rank of its free abelian quotient, called the Betti number. We show that any combination of the group's rank, co-rank, and Betti number within obvious constraints is realized for some finitely presented group (for Betti number equal to rank, the group can be chosen torsion-free). In addition, we show that the Betti number is additive...
Corrections to: “The algebraic topology of smooth algebraic varieties”
Curves and their fundamental groups
Dénombrement des types de K-homotopie. Théorie de la déformation
Die Fundamentalgruppen Siegelscher Modulvarietäten.
Endlichkeits- und Verschwindungssätze für (schwach-) konstruierbare Garbenkomplexe auf komplexen Räumen.
Erratum : Sur le groupe fondamental des schémas analytiques de variété à une dimension
Étale fundamental groups of non-archimedean analytic spaces