Abstract:This paper contains a complete proof of Fukaya and Kato's -isomorphism conjecture for invertible -modules (the case of V = V 0 (r ), where V 0 is unramified of dimension 1). Our results rely heavily on Kato's proof, in an unpublished set of lecture notes, of (commutative) -isomorphisms for one-dimensional representations of G ޑ p , but apart from fixing some sign ambiguities in Kato's notes, we use the theory of (φ, )-modules instead of syntomic cohomology. Also, for the convenience of the reader we give a s… Show more
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