## Regulators, $$L$$-functions and rational points.(English)Zbl 1282.14042

This is an expository paper which introduces the reader to a series of papers by the author and H. Darmon on Kato’s Euler system and rational points on elliptic curves. He points out a remarkable parallelism between the setting of Dirichlet $$L$$-functions and the setting of the $$L$$-functions for elliptic curves. Among other things he focuses on the arithmetic nature of the special values of these $$L$$-functions and describes their connections with the Birch and Swinnerton-Dyer conjecture.

### MSC:

 14G10 Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture) 11G40 $$L$$-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture 11G05 Elliptic curves over global fields

### Keywords:

$$L$$-functions; elliptic curves; Euler systems