Local epsilon isomorphisms

In this paper, we prove the “local ε-isomorphism” conjecture of Fukaya and Kato for a particular class of Galois modules, obtained by interpolating the twists of a fixed crystalline representation of GQp by a family of characters of GQp . This can be regarded as a local analogue of the Iwasawa main conjecture for abelian p-adic Lie extensions of Q p , extending earlier work of Kato for rank one modules, and of Benois and Berger for the cyclotomic extension. We show that such an ε-isomorphism can be constructed using the the 2-variable version of the Perrin-Riou regulator map constructed by the first and third authors