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Annales mathématiques du Québec

, Volume 40, Issue 2, pp 397–434 | Cite as

p-adic families of modular forms and p-adic Abel-Jacobi maps

  • Matthew Greenberg
  • Marco Adamo Seveso
Article

Abstract

We show that p-adic families of modular forms give rise to certain p-adic Abel-Jacobi maps at their p-new specializations. We introduce the concept of differentiation of distributions, using it to give a new description of the Coleman-Teitelbaum cocycle that arises in the context of the \(\mathcal {L}\)-invariant.

Résumé

Nous associons certaines applications p-adiques d’Abel-Jacobi aux familles analytiques de formes modulaires à ses poids nouveaux en p. Nous introduisons le concept de la dérivée d’une distribution. Utilisant ce concept, nous donnons une nouvelle perspective sur le cocycle de Coleman-Teitelbaum dans le contexte de l’invariant \(\mathcal {L}\).

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Copyright information

© Fondation Carl-Herz and Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.Department of Mathematics and StatisticsUniversity of CalgaryCalgaryCanada
  2. 2.Dipartimento di MatematicaUniversità di MilanoMilanItaly

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