A generalization of Darmon’s conjecture for Euler systems for general \(p\)-adic representations. (English) Zbl 1296.11143

Summary: H. Darmon’s conjecture [Can. J. Math. 47, No. 2, 302–317 (1995; Zbl 0844.11071)] on a relation between cyclotomic units over real quadratic fields and certain algebraic regulators was recently solved by B. Mazur and K. Rubin [Compos. Math. 147, No. 1, 56–74 (2011; Zbl 1225.11144)] 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.


11R29 Class numbers, class groups, discriminants
11R27 Units and factorization
11R37 Class field theory
11F85 \(p\)-adic theory, local fields
Full Text: DOI arXiv


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