Galois-theoretic features for 1-smooth pro-p groups
Canadian mathematical bulletin, Tome 65 (2022) no. 2, pp. 525-541
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Let p be a prime. A pro-p group G is said to be 1-smooth if it can be endowed with a continuous representation $\theta \colon G\to \mathrm {GL}_1(\mathbb {Z}_p)$ such that every open subgroup H of G, together with the restriction $\theta \vert _H$, satisfies a formal version of Hilbert 90. We prove that every 1-smooth pro-p group contains a unique maximal closed abelian normal subgroup, in analogy with a result by Engler and Koenigsmann on maximal pro-p Galois groups of fields, and that if a 1-smooth pro-p group is solvable, then it is locally uniformly powerful, in analogy with a result by Ware on maximal pro-p Galois groups of fields. Finally, we ask whether 1-smooth pro-p groups satisfy a “Tits’ alternative.”
Mots-clés :
Galois cohomology, maximal pro-p Galois groups, Bloch–Kato conjecture, Kummerian pro-p pairs, Tits’ alternative
Quadrelli, Claudio. Galois-theoretic features for 1-smooth pro-p groups. Canadian mathematical bulletin, Tome 65 (2022) no. 2, pp. 525-541. doi: 10.4153/S0008439521000461
@article{10_4153_S0008439521000461,
author = {Quadrelli, Claudio},
title = {Galois-theoretic features for 1-smooth pro-p groups},
journal = {Canadian mathematical bulletin},
pages = {525--541},
year = {2022},
volume = {65},
number = {2},
doi = {10.4153/S0008439521000461},
url = {http://geodesic.mathdoc.fr/articles/10.4153/S0008439521000461/}
}
TY - JOUR AU - Quadrelli, Claudio TI - Galois-theoretic features for 1-smooth pro-p groups JO - Canadian mathematical bulletin PY - 2022 SP - 525 EP - 541 VL - 65 IS - 2 UR - http://geodesic.mathdoc.fr/articles/10.4153/S0008439521000461/ DO - 10.4153/S0008439521000461 ID - 10_4153_S0008439521000461 ER -
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