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

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<jats:title>Abstract</jats:title><jats:p>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<jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="gif" xlink:type="simple" xlink:href="S0010437X14007416_inline1" /><jats:tex-math>$2$</jats:tex-math></jats:alternatives></jats:inline-formula>-part’ of Darmon’s conjecture, which was first proved by Mazur and Rubin.</jats:p>

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