Structure of central torsion Iwasawa modules. (English) Zbl 1126.11343

Howson, Susan

Bull. Soc. Math. Fr. 130, No. 4, 507-535 (2002).

Summary: We describe an approach to determining, up to pseudoisomorphism, the structure of a central-torsion module over the Iwasawa algebra of a pro-\(p\), \(p\)-adic, Lie group containing no element of order \(p\). The techniques employed follow classical methods used in the commutative case, but using Ore’s method of localisation. We then consider the properties of certain invariants which may prove useful in determining the structure of a module. Finally, we describe the case of pro-\(p\) subgroups of \(\text{GL}_2 (\mathbb Z_p)\) in detail and give a brief example from the theory of elliptic curves.

MSC:

11R23	Iwasawa theory
16P50	Localization and associative Noetherian rings
22E50	Representations of Lie and linear algebraic groups over local fields

Keywords:

Iwasawa theory; Euler characteristics; Iwasawa modules; structure theory