# Kato’s Euler system and rational points on elliptic curves I: A p-adic Beilinson formula

@article{Bertolini2014KatosES, title={Kato’s Euler system and rational points on elliptic curves I: A p-adic Beilinson formula}, author={Massimo Bertolini and Henri Darmon}, journal={Israel Journal of Mathematics}, year={2014}, volume={199}, pages={163-188} }

This article is the first in a series devoted to Kato’s Euler system arising from p-adic families of Beilinson elements in the K-theory of modular curves. It proves a p-adic Beilinson formula relating the syntomic regulator (in the sense of Coleman-de Shalit and Besser) of certain distinguished elements in the K-theory of modular curves to the special values at integer points ≥ 2 of the Mazur-Swinnerton-Dyer p-adic L-function attached to cusp forms of weight 2. When combined with the explicit…

## 30 Citations

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