-crystals on schemes with constant log structure
-isocrystals and their monodromy groups
-représentations semi-stables
Soient un nombre premier et un corps -adique à corps résiduel parfait (par exemple une extension finie de ) dont l’indice de ramification absolue est noté . Afin d’étudier les « représentations semi-stables de -torsion » de , Breuil a défini pour tout entier positif plusieurs catégories de -modules filtrés de torsion. Dans cet article, nous décrivons la structure de ces catégories dans le cas général (seul le cas avait été étudié de façon systématique jusqu’à présent).
Facteurs locaux des fonctions zêta des variétés algébriques (définitions et conjectures)
Factorial extensions of regular local rings and invariants of finite groups.
Factorial Fermat curves over the rational numbers
A polynomial f in the set {Xⁿ+Yⁿ, Xⁿ +Yⁿ-Zⁿ, Xⁿ +Yⁿ+Zⁿ, Xⁿ +Yⁿ-1} lends itself to an elementary proof of the following theorem: if the coordinate ring over ℚ of f is factorial, then n is one or two. We give a list of problems suggested by this result.
Factorialite de l΄algebre affine de certaines formes quadratiques
Factoring polynomials in finite fields: an application of Lang-Weil to a problem in graph theory.
Factorisation de certains morphismes birationnels
Factorisation faible des applications birationnelles
Factorisation of generalised theta functions. I.
Factorisations explicites de g(y) - h(z)
Factorization estimates for abelian varieties
Factorization of a Birational Morphism Between 4-Folds*.
Factorization of birational morphisms of regular schemes.
Factorization of Birational Morphisms with Fiber Dimension Bounded by 1.
Factorization of nonrigid Zariski dense representations of ... of projective algebraic manifolds.
Factorization of point configurations, cyclic covers, and conformal blocks
We describe a relation between the invariants of ordered points in projective -space and of points contained in a union of two linear subspaces. This yields an attaching map for GIT quotients parameterizing point configurations in these spaces, and we show that it respects the Segre product of the natural GIT polarizations. Associated to a configuration supported on a rational normal curve is a cyclic cover, and we show that if the branch points are weighted by the GIT linearization and the rational...
Factorization of rank two theta functions. II. Proof of the Verlinde formula.
Failure of the Hasse principle for Châtelet surfaces in characteristic
Given any global field of characteristic , we construct a Châtelet surface over that fails to satisfy the Hasse principle. This failure is due to a Brauer-Manin obstruction. This construction extends a result of Poonen to characteristic , thereby showing that the étale-Brauer obstruction is insufficient to explain all failures of the Hasse principle over a global field of any characteristic.