Local Fields and Their Extensions

On fields of algebraic numbers with bounded local degrees

“…For further details on local class field theory we refer to Vostokov and Fesenko's book [4], Ch. IV.…”

Effective lifting of 2-cocycles for Galois cohomology

“…We give a procedure to evaluate local invariants [14,XIII,§ 3] for number fields as stated in Proposition 1.3.…”

Explicit abelian extensions of complete discrete valuation fields

“…We recall that cyclic extensions of K of degree p can be described by means of ArtinSchreier extensions, see [FV,III.2]. Namely, for a cyclic L/K of degree p we have…”