arXiv:0909.3916 Refined class number formulas and Kolyvagin systems from arXiv Front: math.NT by Barry Mazur, Karl Rubin We use the theory of Kolyvagin systems to prove (most of) a refined class number formula conjectured by Darmon. We show that for every odd prime , each side of Darmon’s conjectured formula (indexed by positive integers ) is “almost” a -adic Kolyvagin system as varies. Using the fact that the space of Kolyvagin systems is free of rank one over , we show that Darmon’s formula for arbitrary follows from the case , which in turn follows from classical formulas.
nLab page on Kolyvagin systems