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.


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