A noncommutative Weierstrass preparation theorem and applications to Iwasawa theory
| dc.creator | Venjakob, Otmar | |
| dc.date | 2002-04-12 | |
| dc.date.accessioned | 2026-07-07T04:48:10Z | |
| dc.date.available | 2026-07-07T04:48:10Z | |
| dc.description | In this paper and a forthcoming joint one with Y. Hachimori we study Iwasawa modules over an infinite Galois extension K of a number field k whose Galois group G=G(K/k) is isomorphic to the semidirect product of two copies of the p-adic numbers. After first analyzing some general algebraic properties of the corresponding Iwasawa algebra, we apply these results to the Galois group of the p-Hilbert class field over K. As a main tool we prove a Weierstrass preparation theorem for certain skew power series rings. One striking result in our work is the discovery of the abundance of faithful torsion modules, i.e. non-trivial torsion modules whose global annihilator ideal is zero. Finally we show that the completed group algebra with coefficients in the finite field of p elements is a unique factorization domain in the sense of Chatters. | |
| dc.identifier | https://arxiv.org/abs/math/0204358 | |
| dc.identifier | http://arxiv.org/abs/math/0204358 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/63943 | |
| dc.subject | Number Theory | |
| dc.title | A noncommutative Weierstrass preparation theorem and applications to Iwasawa theory | |
| dc.type | text |