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
Other Sources: http://arxiv.org/abs/0909.3916v1
Terms of Use: This article is made available under the terms and conditions applicable to Open Access Policy Articles, as set forth at http://nrs.harvard.edu/urn-3:HUL.InstRepos:dash.current.terms-of-use#OAP
Citable link to this page: http://nrs.harvard.edu/urn-3:HUL.InstRepos:10076145
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