Sur les formules asymptotiques le long des Zl-extensions

Jean-François Jaulent (1) , Christian Maire (2) , Guillaume Perbet (2)

1 IMB - Institut de Mathématiques de Bordeaux
2 LMB - Laboratoire de Mathématiques de Besançon (UMR 6623)

In this paper we clarify some asymptotic formulas given by Jaulent-Maire, which relate orders of finite quotients of S-infinitesimal T-classes l-groups $Cl^S_T(K_n)$ associated to finite layers $K_n$ of a Zl-extension $K_\infty/K$ over a number field to the structural invariants of the Iwasawa module $X^S_T:=\varprojlim \Cl^S_T(K_n)$. We especially show that the lambda invariant $\tilde\lambda^S_T$ of those quotients sensibly differs from the structural invariant $\lambda^S_T$, and we illustrate this fact with explicit examples, where it can be made as large as desired, positive or negative.

Mots clés: Iwasawa theory; class groups; asymptotic formulas

Domaines: Théorie des nombres [math.NT]

Jean-François Jaulent, Christian Maire, Guillaume Perbet. Sur les formules asymptotiques le long des Zl-extensions. Annales mathématiques du Québec, 2013, 37 (1), pp.63-78. ⟨hal-00632747⟩