Interpolation of Beilinson-Kato elements and $p$-adic $L$-functions

Abstract

Our objective in this series of two articles, of which the present article is the first, is to give a Perrin-Riou-style construction of $p$-adic $L$-functions (of Bellaïche and Stevens) over the eigencurve. As the first ingredient, we interpolate the Beilinson-Kato elements over the eigencurve (including the neighborhoods of $\theta$-critical points). Along the way, we prove étale variants of Bellaïche's results describing the local properties of the eigencurve. We also develop the local framework to construct and establish the interpolative properties of these $p$-adic $L$-functions away from $\theta$-critical points.

49 Pages, final version with title change. May differ from the journal version. To appear in Annales Mathematiques du Quebec (Special birthday issue for Bernadette Perrin-Riou)

References in corpus (1)

• On extra-zeros of p-adic Rankin-Selberg L-functions