TY - JOUR

T1 - Generalised Kawada–Satake method for Mackey functors in class field theory

AU - Fesenko, Ivan B.

AU - Vostokov, Sergei V.

AU - Yoon, Seok Ho

PY - 2018/9/1

Y1 - 2018/9/1

N2 - We propose and study a generalised Kawada–Satake method for Mackey functors in the class field theory of positive characteristic. The root of this method is in the use of explicit pairings, such as the Artin–Schreier–Witt pairing, for groups describing abelian extensions. We separate and simplify the algebraic component of the method and discuss a relation between the existence theorem in class field theory and topological reflexivity with respect to the explicit pairing. We apply this method to derive higher local class field theory of positive characteristic, using advanced properties of topological Milnor K-groups of such fields.

AB - We propose and study a generalised Kawada–Satake method for Mackey functors in the class field theory of positive characteristic. The root of this method is in the use of explicit pairings, such as the Artin–Schreier–Witt pairing, for groups describing abelian extensions. We separate and simplify the algebraic component of the method and discuss a relation between the existence theorem in class field theory and topological reflexivity with respect to the explicit pairing. We apply this method to derive higher local class field theory of positive characteristic, using advanced properties of topological Milnor K-groups of such fields.

KW - Class field theory

KW - Higher class field theory

KW - Higher fields

KW - Reflexivity for non-locally compact groups

KW - Witt vectors

UR - http://www.scopus.com/inward/record.url?scp=85052984553&partnerID=8YFLogxK

U2 - 10.1007/s40879-018-0245-x

DO - 10.1007/s40879-018-0245-x

M3 - Article

AN - SCOPUS:85052984553

VL - 4

SP - 953

EP - 987

JO - European Journal of Mathematics

JF - European Journal of Mathematics

SN - 2199-675X

IS - 3

ER -