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1-SMOOTH PRO-p GROUPS AND BLOCH-KATO PRO-p GROUPS.

Authors :
QUADRELLI, CLAUDIO
Source :
Homology, Homotopy & Applications. 2022, Vol. 24 Issue 2, p53-67. 15p.
Publication Year :
2022

Abstract

Let p be a prime. A pro-p group G is said to be 1-smooth if it can be endowed with a homomorphism of pro-p groups of the form G → 1 + pZp satisfying a formal version of Hilbert 90. By Kummer theory, maximal pro-p Galois groups of fields containing a root of 1 of order p, together with the cyclotomic character, are 1-smooth. We prove that a finitely generated padic analytic pro-p group is 1-smooth if, and only if, it occurs as the maximal pro-p Galois group of a field containing a root of 1 of order p. This gives a positive answer to De Clercq-Florence's "Smoothness Conjecture" -- which states that the surjectivity of the norm residue homomorphism (i.e., the "surjective half" of the Bloch-Kato Conjecture) follows from 1-smoothness -- for the class of finitely generated p-adic analytic pro-p groups. [ABSTRACT FROM AUTHOR]

Details

Language :
English
ISSN :
15320073
Volume :
24
Issue :
2
Database :
Academic Search Index
Journal :
Homology, Homotopy & Applications
Publication Type :
Academic Journal
Accession number :
159485533
Full Text :
https://doi.org/10.4310/HHA.2022.v24.n2.a3