Profinite Groups with a Cyclotomic -Orientation

  • Claudio Quadrelli

    Department of Mathematics and Applications, Università di Milano-Bicocca, Via R. Cozzi 55 - ed. U5, 20125 Milan, Italy
  • Thomas S. Weigel

    Department of Mathematics and Applications, Università di Milano-Bicocca, Via R. Cozzi 55 - ed. U5, 20125 Milan, Italy
Profinite Groups with a Cyclotomic $p$-Orientation cover
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Abstract

Let be a prime. A continuous representation of a profinite group is called a cyclotomic -orientation if for all open subgroups and for all the natural maps are surjective. Here denotes the -module of rank 1 with -action induced by . By the Rost-Voevodsky theorem, the cyclotomic character of the absolute Galois group of a field is, indeed, a cyclotomic -orientation of . We study profinite groups with a cyclotomic -orientation. In particular, we show that cyclotomicity is preserved by several operations on profinite groups, and that Bloch-Kato pro- groups with a cyclotomic -orientation satisfy a strong form of Tits' alternative and decompose as semi-direct product over a canonical abelian closed normal subgroup.

Cite this article

Claudio Quadrelli, Thomas S. Weigel, Profinite Groups with a Cyclotomic -Orientation. Doc. Math. 25 (2020), pp. 1881–1916

DOI 10.4171/DM/788