The equivalence of Rubin’s Conjecture and the ETNC/LRNC for certain biquadratic extensions
نویسنده
چکیده
For an abelian extension L/K of number fields, the Equivariant Tamagawa Number Conjecture at s = 0, which is equivalent to the Lifted Root Number Conjecture, implies Rubin’s Conjecture by work of Burns. 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. 2010 Mathematics Subject Classification: Primary 11R42; Secondary 11R70
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تاریخ انتشار 2013