Ein Analogon zur Fundamentalgruppe einer Riemann'schen Fläche im Zahlköperfall.
Elliptic curves on Abelian surfaces.
Endomorphisms of group schemes and rational points on curves
Equivariant Form of the Deuring-Safarevic Formula for Hasse-Witt Invariants.
Erratum : Sur le groupe fondamental des schémas analytiques de variété à une dimension
Erratum to “Fundamental groups of some special quadric arrangements”.
Etale coverings of a Mumford curve
Let the field be complete w.r.t. a non-archimedean valuation. Let be a Mumford curve, i.e. the irreducible components of the stable reduction of have genus 0. The abelian etale coverings of are constructed using the analytic uniformization and the theta-functions on . For a local field one rediscovers . Frey’s description of the maximal abelian unramified extension of the field of rational functions of .
Étale Galois covers of affine smooth cuves. The geometric case of a conjecture of Shafarevich. On Abhyankar's conjecture.
Explicit Selmer groups for cyclic covers of ℙ¹
For any abelian variety J over a global field k and an isogeny ϕ: J → J, the Selmer group is a subgroup of the Galois cohomology group , defined in terms of local data. When J is the Jacobian of a cyclic cover of ℙ¹ of prime degree p, the Selmer group has a quotient by a subgroup of order at most p that is isomorphic to the ‘fake Selmer group’, whose definition is more amenable to explicit computations. In this paper we define in the same setting the ‘explicit Selmer group’, which is isomorphic...
Exposants -adiques et théorèmes d’indice pour les équations différentielles -adiques