MODULES OVER IWASAWA ALGEBRAS
By John Coates, P. Schneider, R. Sujatha. Journal of the Institute of Mathematics of Jussieu, 2001
83 citations recorded by the source corpus.
Let $G$ be a compact $p$-valued $p$-adic Lie group, and let $\varLambda(G)$ be its Iwasawa algebra. The present paper establishes results about the structure theory of finitely generated torsion $\varLambda(G)$-modules, up to pseudo-isomorphism, which are largely parallel to the classical theory when $G$ is abelian (except for basic differences which occur for those torsion modules which do not possess a non-zero global annihilator). We illustrate our general theory by concrete examples of such modules arising from the Iwasawa theory of elliptic curves without complex multiplication over the field generated by all of their $p$-power torsion points. AMS 2000 Mathematics subject classification: Primary 11G05; 11R23; 16D70; 16E65; 16W70
Subfields: Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/347c286e0d7b58150d3f3425057c7928f7f49110
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Citations in the corpus
- The GL2 Main Conjecture for Elliptic Curves without Complex Multiplication (2004, background): “In the non-commutative case, assuming G is p-valued, it is shown in [7] that there is an exact sequence 0 → ⊕i=1Λ(G)/Li →M/M0 → D → 0,”
- A noncommutative Weierstrass preparation theorem and applications to Iwasawa theory (2002, background): “In [10] they proved that every torsion Λ(G)-module decomposes - up to pseudo-isomorphism - into the direct sum of cyclic modules, where Λ(G) = Zp[[G]] denotes the Iwasawa algebra of a pro-p-group G belonging to a certain class of p-adic groups, viz the class of p-valued ones.”
- Completely Faithful Selmer Groups over Kummer Extensions (2003, background): “Recall that here the cyclicity in the quotient category means that there exists a cyclic submodule C of Xf with pseudo-null cokernel, see [ CSS1 , lem 2.7].”
- Ring-Theoretic Properties of Iwasawa Algebras: A Survey 1 (2005, background): “Since the powerful structural results [15], which can be obtained for certain quotient categories of the category of finitely generated modules over a noetherian maximal order, are potentially important tools in arithmetic applications [18], this question is of more than passing interest.”