Sur les revêtements de Schottky des courbes modulaires de Drinfeld

Discontinuous groups in positive characteristic and automorphisms of Mumford curves

“…They turn out to be Mumford curves for the free group which splits the inclusion Γ(n) tor ✁ Γ(n), where Γ(n) tor is the subgroup generated by torsion elements (cf. Reversat [21]). Proposition 4.…”

Analogue of the degree conjecture over function fields

“…More precisely, one needs an explicit admissible affinoid covering of X an Γ . This is the subject of a paper by Reversat [22]. Associating a formal affine scheme to each of these affinoids in a standard manner, and then gluing those formal affines, one obtains a proper flat one-dimensional formal scheme over Spf(R).…”

On the torsion of Drinfeld modules of rank two

“…Hence the natural map j i : Stab i \Ω i → Γ tor \Ω is an open immersion. By Lemma 2.4 of [23] on page 384 for every i the quotient Stab i \Ω ′ i is analytically isomorphic to a unit disc D i with the origin removed. Let B i be the rigid analytic space Stab i \Ω i ∪ D i obtained by gluing D i with Stab i \Ω i along their common admissible subspace Stab i \Ω ′ i .…”

“…In particular this formal scheme cannot be the formal completion of an algebraic curve over Spec(O ∞ ) along its special fiber. Nevertheless there is a way to obtain a model from this formal scheme, using the work of Reversat in [23]. Next we will give our own account of this theory.…”

“…Hence by Grothendieck's algebraization theorem the formal scheme Γ\ Σ is the formal completion of a projective curve X 0 (p) → Spec(O ∞ ) along its special fiber. According to the main result of [23] (Theorem 2.7 on page 385): Proposition 7.10. The curve X 0 (p) is a totally degenerate semi-stable model of X 0 (p) over the spectrum of O ∞ .…”