The field-of-norms functor and the Hilbert symbol for higher local fields

DOI10.5802/jtnb.786zbMath1286.11204arXiv1010.0555OpenAlexW2963524569MaRDI QIDQ449670

Ruth Jenni, Victor A. Abrashkin

Publication date: 31 August 2012

Published in: Journal de Théorie des Nombres de Bordeaux (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1010.0555

zbMATH Keywords

Hilbert symbolhigher local fieldsfields of normshigher local symbolsVostokov's pairing

Mathematics Subject Classification ID

Galois theory (11S20) Class field theory; (p)-adic formal groups (11S31) (K)-theory of local fields (11S70)

Related Items

Pairings in local fields and cryptography ⋮ Groups of automorphisms of local fields of period \(p^M\) and nilpotent class \(<p\) ⋮ Explicit Serre weights for two-dimensional Galois representations ⋮ An explicit formula for the norm in the theory of fields of norms ⋮ Ramification filtration via deformations ⋮ Shafarevich's paper “A general reciprocity law”

Cites Work

• Galois cohomology and the Brauer group of local fields
• \(p\)-adic étale cohomology
• The field of norms functor and the Brückner-Vostokov formula
• The Hilbert symbol in a complete multidimensional field. I
• Higher fields of norms and \((\varphi,\Gamma)\)-modules
• EXPLICIT CONSTRUCTION OF CLASS FIELD THEORY FOR A MULTIDIMENSIONAL LOCAL FIELD
• EXPLICIT FORM OF THE LAW OF RECIPROCITY
• The explicit reciprocity law and the cohomology of Fontaine-Messing
• The theory of Coleman power series for 𝐾₂
• An analogue of the field-of-norms functor and of the Grothendieck conjecture
• Local class field theory
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