Invitation to higher local fields, Part I, section 2: p-primary part of the Milnor K-groups and Galois cohomology of fields of characteristic p

2000/12/18 by Oleg Izhboldin
Mathematics · #math.NT #math.AG #msc:19F99

paper · pdf

published as Geom. Topol. Monogr. Volume 3(2000) 19-29 · For introduction and notation, see math.NT/0012131 . Published by Geometry and Topology Monographs at http://www.maths.warwick.ac.uk/gt/GTMon3/m3-I-2.abs.html

arxiv created 2000/12/18 · arxiv updated 2009/11/30

Abstract

For an arbitrary field p-torsion and cotorsion of the Milnor groups K_n(F) and K_n^t(F)=K_n(F)/∩_l≥1 lK_n(F) are discussed. The work contains further discussions of an analogue of Satz 90 for K_n(F) and K_n^t(F) and computation of Hⁿ⁺¹_m(F) where F is either the rational function field in one variable F=k(t) or the formal power series F=k((t)).

Related

• Invitation to higher local fields, Part I, section 6: Topological Milnor K-groups of higher local fields
• Galois groups of p-extensions of higher local fields
• Invitation to higher local fields, Part II, section 6: Phi-Gamma-modules and Galois cohomology
• Milnor K₂ and field homomorphisms
• Geometric presentations of Milnor K-groups of certain Artin algebras and Bass-Tate-Kato norms