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THE EQUIVALENCE OF RUBIN'S CONJECTURE AND THE ETNC/LRNC FOR CERTAIN BIQUADRATIC EXTENSIONS

Published online by Cambridge University Press:  13 August 2013

PAUL BUCKINGHAM
PAUL BUCKINGHAM*
Affiliation:
Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton AB, T6G 2G1, Canada e-mail: [email protected]
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Abstract

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For an abelian extension L/K of number fields, the Equivariant Tamagawa Number Conjecture (ETNC) at s = 0, which is equivalent to the Lifted Root Number Conjecture (LRNC), implies Rubin's Conjecture by work of Burns [3]. We show that, for relative biquadratic extensions L/K satisfying a certain condition on the splitting of places, Rubin's Conjecture in turn implies the ETNC/LRNC. We conclude with some examples.

Keywords

Primary 11R42Secondary 11R70
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 56 , Issue 2 , May 2014 , pp. 335 - 353
Copyright
Copyright © Glasgow Mathematical Journal Trust 2013 

References

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