Beilinson-Flach elements and Euler systems I: Syntomic regulators and 𝑝-adic Rankin 𝐿-series

Abstract

This article is the first in a series devoted to the Euler system arising from p p -adic families of Beilinson-Flach elements in the first K K -group of the product of two modular curves. It relates the image of these elements under the p p -adic syntomic regulator (as described by Besser (2012)) to the special values at the near-central point of Hida’s p p -adic Rankin L L -function attached to two Hida families of cusp forms.