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Let be an elliptic curve over with good supersingular reduction at a prime and . We generalise the definition of Kobayashi’s plus/minus Selmer groups over to -adic Lie extensions of containing , using the theory of -modules and Berger’s comparison isomorphisms. We show that these Selmer groups can be equally described using Kobayashi’s conditions via the theory of overconvergent power series. Moreover, we show that such an approach gives the usual Selmer groups in the ordinary case....
Let K/k be a ℤₚ-extension of a number field k, and denote by kₙ its layers. We prove some stabilization properties for the orders and the p-ranks of the higher Iwasawa modules arising from the lower central series of the Galois group of the maximal unramified pro-p-extension of K (resp. of the kₙ).
We describe an approach to determining, up to pseudoisomorphism, the structure of a central-torsion module over the Iwasawa algebra of a pro-, -adic, Lie group containing no element of order . 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- subgroups of in detail and...
In this paper, we study the cohomological dimension of groups , where is the maximal pro--extension of a number field , unramified outside a finite set of places of . This dimension is well-understood only when contains all places above ; in the case where only some of the places above are contained in , one can still obtain some results if contains at least one -extension . Indeed, in that case, the study of the -module allows one to give sufficient conditions for the pro--group...
Nous développons – en nous appuyant sur l’exemple concret des unités cyclotomiques et du groupe de classes en théorie d’Iwasawa cyclotomique – de nouveaux outils pour une étude générale de la descente et de la codescente, dans l’optique de comparer ces deux points de vue duaux.Si est un « système normique » (i.e. une collection de modules galoisiens avec données supplémentaires), attaché à une extension de Lie -adique fixée d’algèbre d’Iwasawa , nous montrons principalement qu’il existe un...
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