Profinite groups with a cyclotomic p-orientation are introduced and studied. The special interest in this class of groups arises from the fact that any absolute Galois group GK of a field K is indeed a profinite group with a cyclotomic p-orientation θK,p:GK→Z×p which is even Bloch-Kato. The same is true for its maximal pro-p quotient GK(p) provided the field K contains a primitive pth-root of unity. The class of cyclotomically p-oriented profinite groups (resp. pro-p groups) which are Bloch-Kato is closed with respect to inverse limits, free product and certain fibre products. For profinite groups with a cyclotomic p-orientation the classical Artin-Schreier theorem holds. Moreover, Bloch-Kato pro-p groups with a cyclotomic orientation satisfy a strong form of Tits' alternative, and the elementary type conjecture formulated by I. Efrat can be restated that the only finitely generated indecomposable torsion free Bloch-Kato pro-p groups with a cyclotomic orientation should be Poincaré duality pro-p groups of dimension less or equal to 2.

Quadrelli, C., Weigel, T. (2020). Profinite Groups with a Cyclotomic p-Orientation. DOCUMENTA MATHEMATICA, 25, 1881-1916 [10.25537/dm.2020v25.1881-1916].

Profinite Groups with a Cyclotomic p-Orientation

Quadrelli, C
;
Weigel, T.
2020

Abstract

Profinite groups with a cyclotomic p-orientation are introduced and studied. The special interest in this class of groups arises from the fact that any absolute Galois group GK of a field K is indeed a profinite group with a cyclotomic p-orientation θK,p:GK→Z×p which is even Bloch-Kato. The same is true for its maximal pro-p quotient GK(p) provided the field K contains a primitive pth-root of unity. The class of cyclotomically p-oriented profinite groups (resp. pro-p groups) which are Bloch-Kato is closed with respect to inverse limits, free product and certain fibre products. For profinite groups with a cyclotomic p-orientation the classical Artin-Schreier theorem holds. Moreover, Bloch-Kato pro-p groups with a cyclotomic orientation satisfy a strong form of Tits' alternative, and the elementary type conjecture formulated by I. Efrat can be restated that the only finitely generated indecomposable torsion free Bloch-Kato pro-p groups with a cyclotomic orientation should be Poincaré duality pro-p groups of dimension less or equal to 2.
Articolo in rivista - Articolo scientifico
Absolute Galois groups, Rost-Voevodsky Theorem, Elementary Type Conjecture, Galois cohomology.
English
nov-2020
2020
25
1881
1916
open
Quadrelli, C., Weigel, T. (2020). Profinite Groups with a Cyclotomic p-Orientation. DOCUMENTA MATHEMATICA, 25, 1881-1916 [10.25537/dm.2020v25.1881-1916].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/294216
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