A generalization of Darmon's conjecture for Euler systems for general p-adic representations

Abstract

Darmon's conjecture on a relation between cyclotomic units over real quadratic fields and certain algebraic regulators was recently solved by Mazur and Rubin by using their theory of Kolyvagin systems. In this paper, we formulate a "non-explicit" version of Darmon's conjecture for Euler systems defined for general $p$-adic representations, and prove it. In the process of the proof, we introduce a notion of "algebraic Kolyvagin systems", and develop their properties.