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

Part of: Algebraic number theory: global fields

Published online by Cambridge University Press:  27 August 2014

T. Sano
T. Sano*
Affiliation:
Department of Mathematics, Keio University, 3-14-1 Hiyoshi, Kohoku-ku, Yokohama, 223-8522, Japan email tkmc310@a2.keio.jp
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Abstract

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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.

Keywords

refined abelian Stark conjectureRubin–Stark conjectureGross’s conjectureDarmon’s conjectureequivariant Tamagawa number conjecture

MSC classification

Primary: 11R42: Zeta functions and $L$-functions of number fields
Secondary: 11R27: Units and factorization 11R29: Class numbers, class groups, discriminants
Type
Research Article
Information
Compositio Mathematica , Volume 150 , Issue 11 , November 2014 , pp. 1809 - 1835
Copyright
© The Author 2014 

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