Hida families, p-adic heights, and derivatives
Annales de l'Institut Fourier, Volume 60 (2010) no. 6, pp. 2275-2299.

This paper concerns the arithmetic of certain p-adic families of elliptic modular forms. We relate, using a formula of Rubin, some Iwasawa-theoretic aspects of the three items in the title of this paper. In particular, we examine several conjectures, three of which assert the non-triviality of an Euler system, a p-adic regulator, and the derivative of a p-adic L-function. We investigate sufficient conditions for the first conjecture to hold and show that, under additional assumptions, the first conjecture implies the equivalence of the last two.

Cet article concerne l’arithmétique de certaines familles p-adiques de formes modulaires elliptiques. En utilisant une formule de Rubin, on examine quelques aspects de la théorie d’Iwasawa pour les objets du titre, dont trois affirment la non-trivialité d’un système d’Euler, d’un régulateur p-adique, et de la dérivée d’une fonction L p-adique. En particulier, on étudie des conditions suffisantes pour que la première conjecture soit vraie et on démontre que, sous des hypothèses supplémentaires, la première conjecture implique que les deux dernières conjectures sont équivalentes.

DOI: 10.5802/aif.2584
Classification: 11R23,  11G40,  11F11,  11S25
Keywords: Iwasawa theory, Hida family, p-adic height, p-adic L-function
Arnold, Trevor 1

1 McMaster University Department of Mathematics & Statistics 1280 Main Street West Hamilton, ON L8S 4K1 (Canada)
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Arnold, Trevor. Hida families, $p$-adic heights, and derivatives. Annales de l'Institut Fourier, Volume 60 (2010) no. 6, pp. 2275-2299. doi : 10.5802/aif.2584. http://www.numdam.org/articles/10.5802/aif.2584/

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