Abelian local \(p\)-class field theory

DOI10.1007/BF01446646zbMath0819.11057WikidataQ56688359 ScholiaQ56688359MaRDI QIDQ1891215

I. B. Fesenko

Publication date: 31 August 1995

Published in: Mathematische Annalen (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/165308

zbMATH Keywords

ramificationcomplete discrete valuation fieldArtin-Schreier extensionsimperfect residue fieldhigher dimensional local fieldsGalois \(p\)-extensionsabelian totally ramified \(p\)-extensionsabstract \(p\)-class field theoryelementary proof of \(p\)-part of class field theorygeneralization of the Hazewinkel homomorphismgeneralization of the Neukirch mapHasse-Herbrand functionHilbert Satz 90Milnor topological \(K\)-groupnorm subgroups

Mathematics Subject Classification ID

Class field theory (11R37) Ramification and extension theory (11S15) Higher symbols, Milnor (K)-theory (19D45) Class field theory; (p)-adic formal groups (11S31) (K)-theory of local fields (11S70) Generalized class field theory ((K)-theoretic aspects) (19F05)

Related Items (9)

Pairings in local fields and cryptography ⋮ Local abelian Kato-Parshin reciprocity law: A survey ⋮ On the properties of the Vostokov and Parshin pairing in higher local class field theory ⋮ Schmid's formula for higher local fields ⋮ Generalized Artin-Hasse and Iwasawa formulas for the Hilbert symbol in a higher local field. II ⋮ Generalised Kawada-Satake method for Mackey functors in class field theory ⋮ Explicit constructions and the arithmetic of local number fields ⋮ Ramification of higher local fields, approaches and questions ⋮ Shafarevich's paper “A general reciprocity law”

Cites Work

• Neubegründung der Klassenkörpertheorie
• Artin-Verdier duality for \(n\)-dimensional local fields involving higher algebraic \(K\)-sheaves
• \(p\)-adic étale cohomology
• A generalization of class formation by using hypercohomology
• Local class field theory is easy
• Micro primes
• Generalized local class field theory. II: Existence theorem. III: Second form of existence theorem. Structure of analytic groups. IV: Cardinalities
• Sur les corps locaux à corps résiduel algébriquement clos
• VECTOR-VALUED DUALITY FOR MODULES OVER BANACH ALGEBRAS
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: Abelian local \(p\)-class field theory