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Global Units modulo Circular Units : descent without Iwasawa's Main Conjecture | Jean-Robert Belliard
; | Date: |
30 Aug 2005 | Subject: | Number Theory MSC-class: 11R23 | math.NT | Abstract: | Iwasawa’s classical asymptotical formula gives the orders of the $p$-parts $X_n$ of the ideal class groups along a $M_p$-extension $F_infty/F$ of a number field $F$. 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 order 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 without using Iwasawa’s Main Conjecture. | Source: | arXiv, math.NT/0508611 | Other source: | [GID 1269727] 0912.2528 | Services: | Forum | Review | PDF | Favorites |
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