Abstract
We study the functional equation for the multi-signed Selmer groups for non-ordinary motives whose Hodge-Tate weights are 0 and 1, defined by Büyükboduk and the first named author. This generalizes simultaneously Greenberg’s result for ordinary motives in and Kim’s result for supersingular elliptic curves.
Résumé
Nous prouvons une équation fonctionnelle pour les groupes de Selmer multi-signés pour les motifs non-ordinaires dont les poids de Hodge-Tate sont 0 et 1, définis par Büyükboduk et le premier auteur. Ce résultat généralise simultanément ceux de Greenberg pour les motifs ordinaires et de Kim pour les courbes elliptiques supersingulières.
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Acknowledgments
The authors would like to thank Kâzım Büyükboduk, Daniel Delbourgo and Florian Sprung for interesting discussion during the preparation of this article. We would also like to thank the anonymous referee for very useful suggestions and comments which led to many improvements on the presentation of the article.
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The authors’ research is supported by the Discovery Grants Program 05710 of NSERC.
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Lei, A., Ponsinet, G. Functional equations for multi-signed Selmer groups. Ann. Math. Québec 41, 155–167 (2017). https://doi.org/10.1007/s40316-016-0063-9
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DOI: https://doi.org/10.1007/s40316-016-0063-9