A generalization of class formation by using hypercohomology.
A generalization of the Hasse-Arf theorem.
Abelian local p-class field theory.
Abstract class field theory (formatting of modules).
Almost -representation. (Presque -représentations.)
An application of the p-adic class number formula.
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...
Arithmetic of formal groups and applications I: Universal norm subgroups.
Associated orders of certain extensions arising from Lubin-Tate formal groups
Let be a finite extension of , let , respectively , be the division fields of level , respectively , arising from a Lubin-Tate formal group over , and let Gal(). It is known that the valuation ring cannot be free over its associated order in unless . We determine explicitly under the hypothesis that the absolute ramification index of is sufficiently large.