THE EQUIVALENCE OF RUBIN'S CONJECTURE AND THE ETNC/LRNC FOR CERTAIN BIQUADRATIC EXTENSIONS
Glasgow mathematical journal, Tome 56 (2014) no. 2, pp. 335-353
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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.
BUCKINGHAM, PAUL. THE EQUIVALENCE OF RUBIN'S CONJECTURE AND THE ETNC/LRNC FOR CERTAIN BIQUADRATIC EXTENSIONS. Glasgow mathematical journal, Tome 56 (2014) no. 2, pp. 335-353. doi: 10.1017/S0017089513000281
@article{10_1017_S0017089513000281,
author = {BUCKINGHAM, PAUL},
title = {THE {EQUIVALENCE} {OF} {RUBIN'S} {CONJECTURE} {AND} {THE} {ETNC/LRNC} {FOR} {CERTAIN} {BIQUADRATIC} {EXTENSIONS}},
journal = {Glasgow mathematical journal},
pages = {335--353},
year = {2014},
volume = {56},
number = {2},
doi = {10.1017/S0017089513000281},
url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089513000281/}
}
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