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On Bloch-Kato's Tamagawa number conjecture for Hecke characters of imaginary quadratic number fields

Bing Han
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Abstract

This is essentially the author's thesis submited to The University of Chicago (May 1997). I prove the validity of Tamagawa number conjecture of Bloch-Kato for certain Hecke characters. I study the exponential map and local Tamagawa number for all odd primes (both ordinary and supersingular), using Kato's explicit reciprocity law for one dimensional Lubin-Tate formal group. I also study p-part of Shafarevich-Tate group for motives associated to Hecke characters, using Rubin's Main Conjecture in Iwasawa theory. Interestingly a congruence property between p-adic periods of elliptic curve and weight 1 Eisenstein series evaluated at torsion CM points play a crucial role in the proof of Bloch-Kato conjecture.

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Bing Han. 1997-07-29. On Bloch-Kato's Tamagawa number conjecture for Hecke characters of imaginary quadratic number fields. https://arxiv.org/abs/math/9707236

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