This article is devoted to some aspects of the algebraic theory of cyclotomic \({\mathbb{Z}}_ p\)-fields \(K=k(\mu_{p^{\infty}})\). The author uses Iwasawa's theory of sheaves for algebraic number fields [\textit{K. Iwasawa}, Ann. Math., II. Ser. 69, 408-413 (1959; Zbl 0090.029)] in order to improve some classical results, and to poke at Greenberg's conjecture from various new perspectives. The main originality of this work is to deal with all the absolute values (i.e., including the Archimedean ones) in the definition of the Pics. By this way, the author is able to generalize \textit{R. Greenberg}'s conjecture [Am. J. Math. 98, 263-284 (1976; Zbl 0334.12013)], some of B. Gross' results [\textit{L. J. Federer} and \textit{B. H. Gross}, Invent. Math. 62, 443-457 (1980; Zbl 0468.12005)], and also the \textit{L. V. Kuz'min}'s duality pairing [Math. USSR, Izv. 14, 441-498 (1980); translation from Izv. Akad. Nauk SSSR, Ser. Mat. 43, 483-546 (1979; Zbl 0434.12006)] from the class of C.M. fields to arbitrary ones. For instance, the generalized Greenberg conjecture is the assertion that the canonical map \[ (*)\quad Pic_ p(K)\quad \to \quad C\ell_ p(K) \] is an isomorphism from the p- part of the Picard group of K onto the p-part of the ideal class group. The author proves that (*) is (almost always) injective, and observes that it is also surjective if one replaces the naive topology in the definition of Pics by the flat quasi-finite Grothendieck topology.