Editing Local field (section)

== Theory of local fields ==
This theory includes the study of types of local fields, extensions of local fields using [[Hensel's lemma]], [[Galois extension]]s of local fields, [[ramification group]]s filtrations of [[Galois group]]s of local fields, the behavior of the norm map on local fields, the local reciprocity homomorphism and existence theorem in [[local class field theory]], [[local Langlands correspondence]], [[Hodge-Tate theory]] (also called [[p-adic Hodge theory|''p''-adic Hodge theory]]), explicit formulas for the [[Hilbert symbol]] in local class field theory, see e.g.{{sfn|Fesenko|Vostokov|2002|loc=Chapters 1-4, 7}}