Le plongement caloisien à noyau d'ordre premier et ses applications à la construction d'extensions non abéliennes
Lifting the field of norms
Let be a finite extension of . The field of norms of a -adic Lie extension is a local field of characteristic which comes equipped with an action of . When can we lift this action to characteristic , along with a compatible Frobenius map? In this note, we formulate precisely this question, explain its relevance to the theory of -modules, and give a condition for the existence of certain types of lifts.
Local Class Field Theory via Lubin-Tate Theory
We give a self-contained exposition of local class field theory, via Lubin-Tate theory and the Hasse-Arf theorem, refining the arguments of Iwasawa [9].
Local Leopoldt's problem for rings of integers in Abelian -extensions of complete discrete valuation fields.
Local p-dimensional Galois characters.
Logarithme p-adique, p-ramification abélienne et K ...
Modified proof of a local analogue of the Grothendieck conjecture
A local analogue of the Grothendieck Conjecture is an equivalence between the category of complete discrete valuation fields with finite residue fields of characteristic and the category of absolute Galois groups of fields together with their ramification filtrations. The case of characteristic 0 fields was studied by Mochizuki several years ago. Then the author of this paper proved it by a different method in the case (but with no restrictions on the characteristic of ). In this paper...
Modules galoisiens de torsion et dualité.
New ramification breaks and additive Galois structure
Which invariants of a Galois -extension of local number fields (residue field of char , and Galois group ) determine the structure of the ideals in as modules over the group ring , the -adic integers? We consider this question within the context of elementary abelian extensions, though we also briefly consider cyclic extensions. For elementary abelian groups , we propose and study a new group (within the group ring where is the residue field) and its resulting ramification filtrations....
Normal integral bases and complex conjugation.
Number fields with the same index
Okutsu invariants and Newton polygons
On 2-extensions of the rationals with restricted ramification
For a finite group G let 𝒦₂(G) denote the set of normal number fields (within ℂ) with Galois group G which are 2-ramified, that is, unramified outside {2,∞}. We describe the 2-groups G for which 𝒦₂(G) ≠ ∅, and determine the fields in 𝒦₂(G) for certain distinguished 2-groups G appearing (dihedral, semidihedral, modular and semimodular groups). Our approach is based on Fröhlich's theory of central field extensions, and makes use of ring class field constructions (complex multiplication).
On extensions of number fields obtained by specializing branched coverings.
On general local reciprocity maps.
On norm maps for one dimensional formal groups. II. ...-extensions of local fields with algebraically closed residue field.
On semicontinuity of ramification invariants in dimension 2.
On the cyclicity of a Galois module in local fields.
On the genus group of algebraic number fields
On the Iwasawa invariants of certain -extensions