Global Units modulo Circular Units : descent without Iwasawa's Main Conjecture
| dc.creator | Belliard, Jean-Robert | |
| dc.date | 2005-08-30 | |
| dc.date | 2006-10-11 | |
| dc.date.accessioned | 2026-07-07T06:42:52Z | |
| dc.date.available | 2026-07-07T06:42:52Z | |
| dc.description | Iwasawa's classical asymptotical formula relates the orders of the $p$-parts $X_n$ of the ideal class groups along a $\ZM_p$-extension $F_\infty/F$ of a number field $F$, to Iwasawa structural invariants $\la$ and $μ$ attached to the inverse limit $X_\infty=\limpro X_n$. It relies on "good" descent properties satisfied by $X_n$. If $F$ is abelian and $F_\infty$ is cyclotomic it is known that the $p$-parts of the orders of the global units modulo circular units $U_n/C_n$ are asymptotically equivalent to the $p$-parts of the ideal class numbers. This suggests that these quotients $U_n/C_n$, so to speak unit class groups, satisfy also good descent properties. We show this directly, i.e. without using Iwasawa's Main Conjecture. | |
| dc.description | 18 pages. Enlarged fonts, corrected a few typos. Accepted for publication in Canadian Journal of Mathematic | |
| dc.identifier | https://arxiv.org/abs/math/0508611 | |
| dc.identifier | http://arxiv.org/abs/math/0508611 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/102204 | |
| dc.subject | Number Theory | |
| dc.subject | 11R23 | |
| dc.title | Global Units modulo Circular Units : descent without Iwasawa's Main Conjecture | |
| dc.type | text |