Signed Selmer groups over p-adic Lie extensions
Journal de Théorie des Nombres de Bordeaux, Volume 24 (2012) no. 2, pp. 377-403.

Let E be an elliptic curve over with good supersingular reduction at a prime p3 and a p =0. We generalise the definition of Kobayashi’s plus/minus Selmer groups over (μ p ) to p-adic Lie extensions K of containing (μ p ), using the theory of (ϕ,Γ)-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.

Soit E une courbe elliptique définie sur ayant bonne réduction supersingulière en p, où p est un nombre premier impair et a p =0. En utilisant la théorie des (ϕ,Γ)-modules et le théorème de comparaison de Berger, nous généralisons la définition des groupes de Selmer plus et moins sur l’extension (μ p ) aux extensions de Lie p-adiques K de qui contiennent (μ p ). Nous montrons que ces groupes de Selmer peuvent également être dé-crits par les conditions de Kobayashi via la théorie des séries surconvergentes. De plus, nous montrons qu’on récupère les groupes de Selmer habituels dans le cas ordinaire avec notre approche.

Received:
Published online:
DOI: 10.5802/jtnb.802
Antonio Lei 1; Sarah Livia Zerbes 2

1 School of Mathematical Sciences Monash University Clayton, VIC 3800 Australia Since December 2011 : Department of Mathematics and Statistics Burnside Hall McGill University Montreal QC Canada H3A 2K6
2 Department of Mathematics Harrison Building University of Exeter Exeter EX4 4QF, UK
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Antonio Lei; Sarah Livia Zerbes. Signed Selmer groups over $p$-adic Lie extensions. Journal de Théorie des Nombres de Bordeaux, Volume 24 (2012) no. 2, pp. 377-403. doi : 10.5802/jtnb.802. https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.802/

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