Centres of skewfields and completely faithful Iwasawa modules
| Autor: | Konstantin Ardakov |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2016 |
| Předmět: |
Discrete mathematics
Pure mathematics Mathematics - Number Theory Selmer group Mathematics::Number Theory General Mathematics Iwasawa theory Elliptic curve Mathematics::K-Theory and Homology Iwasawa algebra Lie algebra FOS: Mathematics Torsion (algebra) Number Theory (math.NT) Finitely-generated abelian group 11G05 11R23 12E15 16D70 Quotient Mathematics |
| Popis: | Let H be a torsionfree compact p-adic analytic group whose Lie algebra is split semisimple. We show that the quotient skewfield of fractions of the Iwasawa algebra \Lambda_H of H has trivial centre and use this result to classify the prime c-ideals in the Iwasawa algebra \Lambda_G of G := H \times \Zp. We also show that a finitely generated torsion \Lambda_G-module having no non-zero pseudo-null submodule is completely faithful if and only if it is has no central torsion. This has an application to the study of Selmer groups of elliptic curves. |
| Databáze: | OpenAIRE |
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