Geodesic
Profinite Groups with a Cyclotomic $p$-Orientation
Documenta mathematica, Tome 25 (2020), pp. 1881-1916
Cet article a éte moissonné depuis la source EMS Press

Voir la notice de l'article

Let p be a prime. A continuous representation θ:G→GL1​(Zp​) of a profinite group G is called a cyclotomic p-orientation if for all open subgroups U⊆G and for all k,n≥1 the natural maps Hk(U,Zp​(k)/pn)→Hk(U,Zp​(k)/p) are surjective. Here Zp​(k) denotes the Zp​-module of rank 1 with U-action induced by θ∣Uk​. By the Rost-Voevodsky theorem, the cyclotomic character of the absolute Galois group GK​ of a field K is, indeed, a cyclotomic p-orientation of GK​. We study profinite groups with a cyclotomic p-orientation. In particular, we show that cyclotomicity is preserved by several operations on profinite groups, and that Bloch-Kato pro-p groups with a cyclotomic p-orientation satisfy a strong form of Tits' alternative and decompose as semi-direct product over a canonical abelian closed normal subgroup.
DOI : 10.4171/dm/788
Classification : 12F10, 12G05, 20E18
Mots-clés : absolute Galois groups, Rost-Voevodsky theorem, elementary type conjecture 
@article{10_4171_dm_788,
     author = {Claudio Quadrelli and Thomas S. Weigel},
     title = {Profinite {Groups} with a {Cyclotomic} $p${-Orientation}},
     journal = {Documenta mathematica},
     pages = {1881--1916},
     year = {2020},
     volume = {25},
     doi = {10.4171/dm/788},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/788/}
}
TY  - JOUR
AU  - Claudio Quadrelli
AU  - Thomas S. Weigel
TI  - Profinite Groups with a Cyclotomic $p$-Orientation
JO  - Documenta mathematica
PY  - 2020
SP  - 1881
EP  - 1916
VL  - 25
UR  - http://geodesic.mathdoc.fr/articles/10.4171/dm/788/
DO  - 10.4171/dm/788
ID  - 10_4171_dm_788
ER  - 
%0 Journal Article
%A Claudio Quadrelli
%A Thomas S. Weigel
%T Profinite Groups with a Cyclotomic $p$-Orientation
%J Documenta mathematica
%D 2020
%P 1881-1916
%V 25
%U http://geodesic.mathdoc.fr/articles/10.4171/dm/788/
%R 10.4171/dm/788
%F 10_4171_dm_788
Claudio Quadrelli; Thomas S. Weigel. Profinite Groups with a Cyclotomic $p$-Orientation. Documenta mathematica, Tome 25 (2020), pp. 1881-1916. doi: 10.4171/dm/788

Cité par Sources :