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2-Cohomology of semi-simple simply connected group-schemes over curves defined over $p$ -adic fields

Jean-Claude Douai (2013)

Journal de Théorie des Nombres de Bordeaux

Let $X$ be a proper, smooth, geometrically connected curve over a $p$ -adic field $k$ . Lichtenbaum proved that there exists a perfect duality: $Br (X) \times Pic (X) \to ℚ / ℤ$ between the Brauer and the Picard group of $X$ , from which he deduced the existence of an injection of $Br (X)$ in $\prod_{P \in X} Br (k_{P})$ where $P \in X$ and $k_{P}$ denotes the residual field of the point $P$ . The aim of this paper is to prove that if $G = \tilde{G}$ is an $X_{e t}$ - scheme of semi-simple simply connected groups (s.s.s.c groups), then we can deduce from Lichtenbaum’s results the neutrality of every $X_{e t}$ -gerb which...

A basis for the non-archimedean holomorphic theta functions.

Van Steen, G. (1994)

Bulletin of the Belgian Mathematical Society - Simon Stevin

A descent map for curves with totally degenerate semi-stable reduction

Shahed Sharif (2013)

Journal de Théorie des Nombres de Bordeaux

Let $K$ be a local field of residue characteristic $p$ . Let $C$ be a curve over $K$ whose minimal proper regular model has totally degenerate semi-stable reduction. Under certain hypotheses, we compute the prime-to- $p$ rational torsion subgroup on the Jacobian of $C$ . We also determine divisibility of line bundles on $C$ , including rationality of theta characteristics and higher spin structures. These computations utilize arithmetic on the special fiber of $C$ .

A generalization of formal schemes and rigid analytic varieties.

R. Huber (1994)

Mathematische Zeitschrift

A new construction of $p$ -adic $L$ -functions attached to certain elliptic curves with complex multiplication

John L. Boxall (1986)

Annales de l'institut Fourier

In this paper we apply the results of our previous article on the $p$ -adic interpolation of logarithmic derivatives of formal groups to the construction of $p$ -adic $L$ -functions attached to certain elliptic curves with complex multiplication. Our results are primarily concerned with curves with supersingular reduction.

A Note on the First Rigid Cohomology Group for Geometrically Unibranch Varieties

Nobuo TSUZUKI (2012)

Rendiconti del Seminario Matematico della Università di Padova

À propos de G. A. G. R.

Pierre Jarraud (1983/1984)

Groupe de travail d'analyse ultramétrique

A Rigid Analytic Version of M. Artin's Theorem on Analytic Equations.

Siegfried Bosch (1981)

Mathematische Annalen

A weak Néron model with applications to $p$ -adic dynamical systems

Liang-Chung Hsia (1996)

Compositio Mathematica

Action du groupe de Galois sur les périodes de certaines courbes de Mumford

Christophe Brouillard (1994)

Journal de théorie des nombres de Bordeaux

Nous étudions l’action du groupe de Galois sur les périodes des courbes de Mumford qui sont des revêtements cycliques de $ℙ_{K}^{1}$ . Lorsque le degré de ce revêtement est premier à la caractéristique résiduelle du corps de base, nous décomposons le réseau des périodes en une somme directe de modules monogènes, le nombre de ces modules monogènes étant déduit de la géométrie de la courbe (théorème 4). Ceci nous permet de donner une condition nécessaire et suffisante pour que le module des périodes soit libre...