Algèbre d'Iwasawa
Algèbre du groupe infini ... et produit tensoriel de corps valués.
Algèbres -adiques
Almost -representation. (Presque -représentations.)
An algorithm for finding distinguished chains of polynomials.
An algorithmic construction of cyclic p-extensions of fields, with characteristic different from p, not containing the pth roots of unity
An application of the p-adic class number formula.
An elementary proof of the Mazur-Tate-Teitelbaum conjecture for elliptic curves.
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 2nth reciprocity law.
An explicit Brauer formula for local Galois characters.
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...
An extension of Iwasawa's theorem on finitely generated modules over power series rings.
An extension of -zeta function.
An extension of the Apéry number supercongruence
An infinite dimensional Hodge-Tate theory
An irreducibility criterion for composition of polynomials.
Analogs of Bernoulli polynomials in fields Zp.
Analogues -adiques de certaines fonctions arithmétiques
Analogues p-adiques de certaines fonctions arithmétiques.