1-motivi di varietà proiettive semplicemente connesse e scoppiamenti
A Gauss-Bonnet theorem for motivic cohomology.
A generalisation of the Cassel-Tate pairing.
A genericity theorem for algebraic stacks and essential dimension of hypersurfaces
We compute the essential dimension of the functors Forms and Hypersurf of equivalence classes of homogeneous polynomials in variables and hypersurfaces in , respectively, over any base field of characteristic . Here two polynomials (or hypersurfaces) over are considered equivalent if they are related by a linear change of coordinates with coefficients in . Our proof is based on a new Genericity Theorem for algebraic stacks, which is of independent interest. As another application of the...
A Lefschetz decomposition for Chow motives of abelian schemes.
A note on indecomposable motivic cohomology classes.
A note on tangent bundles in a category with a ring object.
Alcune proprietà degli spazi algebrici
Algebraizitätskriterien für holomorphe Abbildungen zwischen algebraischen Räumen.
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...
Analytic functions on an open subsets of P1 (k).
Arithmetic vector bundles and automorphic forms on Shimura varieties, II
Chow Motif and Higher Chow Theory of G/P.
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.
Comparison theorems for Gromov–Witten invariants of smooth pairs and of degenerations
We consider four approaches to relative Gromov–Witten theory and Gromov–Witten theory of degenerations: J. Li’s original approach, B. Kim’s logarithmic expansions, Abramovich–Fantechi’s orbifold expansions, and a logarithmic theory without expansions due to Gross–Siebert and Abramovich–Chen. We exhibit morphisms relating these moduli spaces and prove that their virtual fundamental classes are compatible by pushforward through these morphisms. This implies that the Gromov–Witten invariants associated...
Connected algebraic monoids.
Corrigendum to : « Tame stacks in positive characteristic »
de Rham Theory for Tame Stacks and Schemes with Linearly Reductive Singularities
We prove that the Hodge-de Rham spectral sequence for smooth proper tame Artin stacks in characteristic (as defined by Abramovich, Olsson, and Vistoli) which lift mod degenerates. We push the result to the coarse spaces of such stacks, thereby obtaining a degeneracy result for schemes which are étale locally the quotient of a smooth scheme by a finite linearly reductive group scheme.
Descent, motives and K-theory.
Dilogarithm, grassmannian complex and scissors congruence groups of algebraic polyhedra