Abstract
Given a rank two trianguline family of \((\varphi ,\Gamma )\)-modules having a noncrystalline semistable member, we compute the Fontaine–Mazur \({\mathcal {L}}\)-invariant of that member in terms of the logarithmic derivative, with respect to the Sen weight, of the value at p of the trianguline parameter. This generalizes prior work, in the case of Galois representations, due to Greenberg–Stevens and Colmez.
Résumé
Étant donnée une famille trianguline de rang deux de modules \((\phi ,\Gamma )\) dont un membre est semi-stable non cristallin, nous calculons l’invariant-\({\mathcal {L}}\) de Fontaine-Mazur de ce membre en fonction de la dérivée logarithmique, par rapport au poids de Sen, de la valeur du paramètre triangulin pour p. Il s’agit d’une généralisation d’un travail antérieur dans le cas de représentations de Galois, dû à Greenberg-Stevens et Colmez.
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Dedicated to Glenn Stevens on the occasion of his 60th birthday.
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Pottharst, J. The \({\mathcal {L}}\)-invariant, the dual \({\mathcal {L}}\)-invariant, and families. Ann. Math. Québec 40, 159–165 (2016). https://doi.org/10.1007/s40316-015-0054-2
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DOI: https://doi.org/10.1007/s40316-015-0054-2