  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.
