This paper is a sequel to our earlier paper "Wach modules and Iwasawa theory
for modular forms" (arXiv: 0912.1263), where we defined a family of Coleman
maps for a crystalline representation of the Galois group of Qp with
nonnegative Hodge-Tate weights. In this paper, we study these Coleman maps
using Perrin-Riou's p-adic regulator L_V. Denote by H(\Gamma) the algebra of
Qp-valued distributions on \Gamma = Gal(Qp(\mu (p^\infty) / Qp). Our first
result determines the H(\Gamma)-elementary divisors of the quotient of
D_{cris}(V) \otimes H(\Gamma) by the H(\Gamma)-submodule generated by (\phi *
N(V))^{\psi = 0}, where N(V) is the Wach module of V. By comparing the
determinant of this map with that of L_V (which can be computed via
Perrin-Riou's explicit reciprocity law), we obtain a precise description of the
images of the Coleman maps. In the case when V arises from a modular form, we
get some stronger results about the integral Coleman maps, and we can remove
many technical assumptions that were required in our previous work in order to
reformulate Kato's main conjecture in terms of cotorsion Selmer groups and
bounded p-adic L-functions.Comment: 27 page
