  In this paper, we prove the "local epsilon-isomorphism conjecture" of Fukaya
and Kato for a particular class of Galois modules obtained by tensoring a
Zp-lattice in a crystalline representation of the Galois group of Qp with a
representation of an abelian quotient of the Galois group with values in a
suitable p-adic local ring. This can be regarded as a local analogue of the
Iwasawa main conjecture for abelian p-adic Lie extensions of Qp, extending
earlier work of Benois and Berger for the cyclotomic extension. We show that
such an epsilon-isomorphism can be constructed using the Perrin-Riou regulator
map, or its extension to the 2-variable case due to the first and third
authors.
