Galois Coverings of the Non-Archimedean Projective Line.
Géométrie rigide et cohomologie des variétés algébriques de caractéristique p
Géométrie rigide et cohomologie des variétés algébriques de caractéristique
Geometry of an étale covering of the -adic upper half plane
We describe the rigid geometry of the first layer in the tower of coverings of the -adic upper half plane constructed by Drinfeld. Using our results, we describe the stable fiber at p of certain Shimura curves.
Greatest common divisors of , in positive characteristic and rational points on curves over finite fields
In our previous work we proved a bound for the , for -units of a function field in characteristic zero. This generalized an analogous bound holding over number fields, proved in [3]. As pointed out by Silverman, the exact analogue does not work for function fields in positive characteristic. In the present work, we investigate possible extensions in that direction; it turns out that under suitable assumptions some of the results still hold. For instance we prove Theorems 2 and 3 below, from...