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