Abelian extensions of an absolutely unramified local field with general residue field.
Almost -representation. (Presque -représentations.)
An equicharacteristic analogue of Hesselholt's conjecture on cohomology of Witt vectors
Let L/K be a finite Galois extension of complete discrete valued fields of characteristic p. Assume that the induced residue field extension is separable. For an integer n ≥ 0, let denote the ring of Witt vectors of length n with coefficients in . We show that the proabelian group is zero. This is an equicharacteristic analogue of Hesselholt’s conjecture, which was proved before when the discrete valued fields are of mixed characteristic.
An explicit formula for the Hilbert symbol of a formal group
A Brückner-Vostokov formula for the Hilbert symbol of a formal group was established by Abrashkin under the assumption that roots of unity belong to the base field. The main motivation of this work is to remove this hypothesis. It is obtained by combining methods of ()-modules and a cohomological interpretation of Abrashkin’s technique. To do this, we build ()-modules adapted to the false Tate curve extension and generalize some related tools like the Herr complex with explicit formulas for the...
-représentations dans le cas relatif
Dans ce travail nous développons un analogue relatif de la théorie de Sen pour les -représentations. On donne des applications à la théorie des représentations -adiques, en la reliant à la théorie des -modules relatifs, et à celle des modules de Higgs -adiques développée par G. Faltings.
Berichtigung zu den Arbeiten "Einbettungsprobleme und Galoisstruktur lokaler Körper" und "Abelsche p-Erweiterungen p-adischer Zahlkörper, über denen jedes Einbettungsproblem lösbar ist".
Bloch and Kato's exponential map: three explicit formulas.
Cohomological Dimension of Local Fields.
Cohomology groups of the class groups over a ℤₚ extension
Continuous Cohomology and p-Adic Galois Representations.
Der Eindeutigkeitssatz für Demuskinformationen.
Die Struktur der absoluten Galoisgruppe p-adischer Körper.
Einbettungsprobleme und Galoisstruktur lokaler Körper.
Exercises dyadiques.
Fonctions -adiques d’une courbe elliptique et points rationnels
On construit une fonction -adique arithmétique associée à une courbe elliptique ayant bonne réduction en , fonction à valeurs dans son module de Dieudonné en . On donne le lien conjectural avec les fonctions de Mazur et Swinnerton-Dyuer d’une part et les éléments de Beilinson-Kato d’autre part et on énonce une conjecture principale". On calcule aussi les termes dominants de cette fonction -adique aux entiers en liaison avec les conjectures -adiques du tupe Birch et Swinnerton-Dyer et Bloch-Kato....
Galois cohomology and Galois representations.
Height pairings in families of deformations.
Hida families, -adic heights, and derivatives
This paper concerns the arithmetic of certain -adic families of elliptic modular forms. We relate, using a formula of Rubin, some Iwasawa-theoretic aspects of the three items in the title of this paper. In particular, we examine several conjectures, three of which assert the non-triviality of an Euler system, a -adic regulator, and the derivative of a -adic -function. We investigate sufficient conditions for the first conjecture to hold and show that, under additional assumptions, the first...
Higher fields of norms and -modules.
Hilbert symbols as maps of functors