  As remarked in [Kolyvagin systems, by Barry Mazur and Karl Rubin] Proposition
6.2.6 and Buyukboduk[ arXiv:0706.0377v1 ] Remark 3.25 one does not expect the
Kolyvagin system obtained from an Euler system for a p-adic Galois
representation T to be primitive (in the sense of [Kolyvagin systems, by Barry
Mazur and Karl Rubin] Definition 4.5.5) if p divides a Tamagawa number at a
prime \ell different from p; thus fails to compute the correct size of the
relevant Selmer module. In this paper we obtain a lower bound for the size of
the cokernel of the Euler system to Kolyvagin system map (see Theorem 3.2.4 of
[Kolyvagin systems, by Barry Mazur and Karl Rubin] for a definition of this
map) in terms of the Tamagawa numbers of T, refining [Kolyvagin systems, by
Barry Mazur and Karl Rubin] Propostion 6.2.6. We show how this partially
accounts for the missing Tamagawa factors in Kato's calculations with his Euler
system.
