Substitutions de séries formelles et cyclotomie

✍ Scribed by F. Laubie; A. Movahhedi

• Book ID: 102974200
• Publisher: Elsevier Science
• Year: 1996
• Tongue: English
• Weight: 568 KB
• Volume: 58
• Category: Article
• ISSN: 0022-314X
• DOI: 10.1006/jnth.1996.0076

✦ Synopsis

Let F q be the finite field with q=p f elements. Let 1 be the closed subgroup generated by a series #(t) # t+t 2 F q [[t]] of infinite order for the substitution law, and let 4=Z p [[1]] be the Iwasawa algebra of 1. The multiplicative group U=1+tF q [[t]] is a right 1-module by substitution. We give a necessary and sufficient condition on the ramification of #(t) for which the 4-module U is noetherian and, in this case, we describe its structure. In particular, we prove that U possesses a non trivial 4-torsion if and only if there exists a series s(t) # tF q [[t]] and a p-adic unit u such that s b #(t)=(1+s(t)) u &1.