Refined Class Number Formulas and Kolyvagin Systems

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Refined Class Number Formulas and Kolyvagin Systems

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Title: Refined Class Number Formulas and Kolyvagin Systems
Author: Rubin, Karl; Mazur, Barry C.

Note: Order does not necessarily reflect citation order of authors.

Citation: Mazur, Barry, and Karl Rubin. 2011. Refined class number formulas and Kolyvagin systems. Compositio Mathematica 147(1): 56-74.
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Abstract: 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 \(p\), each side of Darmon’s conjectured formula (indexed by positive integers \(n\) is “almost” a \(p\)-adic Kolyvagin system as \(n\) varies. Using the fact that the space of Kolyvagin systems is free of rank one over Z\(_p\), we show that Darmon’s formula for arbitrary \(n\) follows from the case \(n\) = 1, which in turn follows from classical formulas.
Published Version: doi://10.1112/S0010437X1000494X
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