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On congruence relations between the fundamental units of biquadratic fields

✍ Scribed by Sey Kim

Publisher
Elsevier Science
Year
2006
Tongue
English
Weight
249 KB
Volume
121
Category
Article
ISSN
0022-314X

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✦ Synopsis

Given any distinct prime numbers p, q, and r satisfying certain simple congruence conditions, we display a congruence relation between the fundamental units for the biquadratic field K = Q( √ pr, √ q ), modulo a certain prime ideal of O K . This congruence in particular implies the validity of the equivariant Tamagawa number conjecture formulated by Burns and Flach for the pair (h 0 (Spec K), Z[Gal(K/Q)]).

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