Refined abelian Stark conjectures and the equivariant leading term conjecture of Burns

Publisher: Cambridge University Press

E-ISSN: 1570-5846|150|11|1809-1835

ISSN: 0010-437x

Source: Compositio Mathematica, Vol.150, Iss.11, 2014-11, pp. : 1809-1835

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Abstract

We formulate a conjecture which generalizes Darmon’s ‘refined class number formula’. We discuss relations between our conjecture and the equivariant leading term conjecture of Burns. As an application, we give another proof of the ‘except $2$ -part’ of Darmon’s conjecture, which was first proved by Mazur and Rubin.