Proof of the Main Conjecture of Noncommutative Iwasawa Theory for Totally Real Number Fields in Certain Cases
| dc.creator | Kakde, Mahesh | |
| dc.date | 2008-02-15 | |
| dc.date | 2008-02-18 | |
| dc.date.accessioned | 2026-07-07T09:21:15Z | |
| dc.date.available | 2026-07-07T09:21:15Z | |
| dc.description | Fix an odd prime $p$. Let $G$ be a compact $p$-adic Lie group containing a closed, normal, pro-$p$ subgroup $H$ which is abelian and such that $G/H$ is isomorphic to the additive group of $p$-adic integers $\mathbbZ_p$ . First we assume that $H$ is finite and compute the Whitehead group of the Iwasawa algebra, $Λ(G)$, of $G$. We also prove some results about certain localisation of $Λ(G)$ needed in Iwasawa theory. Let $F$ be a totally real number field and let $F_{\infty}$ be an admissible $p$-adic Lie extension of $F$ with Galois group $G$. The computation of the Whitehead groups are used to show that the Main Conjecture for the extension $F_{\infty}/F$ can be deduced from certain congruences between abelian $p$-adic zeta functions of Delige and Ribet. We prove these congruences with certain assumptions on $G$. This gives a proof of the Main Conjecture in many interesting cases such as $\mathbb{Z}_p\rtimes | |
| dc.description | 49 pages | |
| dc.identifier | https://arxiv.org/abs/0802.2272 | |
| dc.identifier | http://arxiv.org/abs/0802.2272 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/154956 | |
| dc.subject | Number Theory | |
| dc.subject | 11R23; 11R80 | |
| dc.title | Proof of the Main Conjecture of Noncommutative Iwasawa Theory for Totally Real Number Fields in Certain Cases | |
| dc.type | text |