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Article Dans Une Revue Canadian Journal of Mathematics = Journal Canadien de Mathématiques Année : 2009

Global Units modulo Circular Units : descent without Iwasawa's Main Conjecture.

Résumé

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 $\mu$ 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.
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Dates et versions

hal-00440905 , version 1 (13-12-2009)

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Citer

Jean-Robert Belliard. Global Units modulo Circular Units : descent without Iwasawa's Main Conjecture.. Canadian Journal of Mathematics = Journal Canadien de Mathématiques, 2009, 61 (3), pp.518--533. ⟨hal-00440905⟩
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