nLab Iwasawa algebra

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Idea

The Iwasawa algebra, classically, is the completed group ring p[[Γ]]\mathbb{Z}_{p}[[\Gamma]], where Γ\Gamma is the subgroup of Gal((μ p )/) p ×\Gal(\mathbb{Q}(\mu_{p^{}\infty})/\mathbb{Q})\cong \mathbb{Z}_{p}^{\times} which is isomorphic to 1+p p1+p\mathbb{Z}_{p}. The Iwasawa algebra is also isomorphic to the power series ring p[[T]]\mathbb{Z}_{p}[[T]].

References

  • K. Ardakov, K. A. Brown, Ring-theoretic properties of Iwasawa algebras: a survey, Documenta Mathematica, Extra Volume: John H. Coates’ Sixtieth Birthday (2006), 7-33 link

See also:

Last revised on December 6, 2022 at 17:00:29. See the history of this page for a list of all contributions to it.