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The main result of this paper implies that if an abelian variety over a field has a maximal isotropic subgroup of -torsion points all of which are defined over , and , then the abelian variety has semistable reduction away from . This result can be viewed as an extension of Raynaud’s theorem that if an abelian variety and all its -torsion points are defined over a field and , then the abelian variety has semistable reduction away from . We also give information about the Néron models...
Classical sieve methods of analytic number theory have recently been adapted to a geometric setting. In the new setting, the primes are replaced by the closed points of a variety over a finite field or more generally of a scheme of finite type over . We will present the method and some of the surprising results that have been proved using it. For instance, the probability that a plane curve over is smooth is asymptotically as its degree tends to infinity. Much of this paper is an exposition...
En utilisant le théorème de Christol, Kamae, Mendès France et Rauzy, nous donnons une démonstration élémentaire de la transcendance de la série formelle ainsi que d’autres séries formelles à coefficients dans un corps fini.
Afin de disposer des opérations cohomologiques aussi souples que possible pour la cohomologie de de Rham -adique, le but principal de ce mémoire est de résoudre intrinsèquement du point de vue cohomologique le problème des relèvements des schémas lisses et de leurs morphismes de la caractéristique à la caractéristique nulle ce qui a été l’une des difficultés centrales de la théorie de la cohomologie de de Rham des schémas algébriques en caractéristique positive depuis le début. Nous montrons...
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