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arXiv · 1303.1785

Local epsilon isomorphisms

David Loeffler·Sarah Livia Zerbes·Otmar Venjakob
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Abstract

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.

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David Loeffler, Sarah Livia Zerbes, Otmar Venjakob. 2013-03-07. Local epsilon isomorphisms. https://doi.org/10.1215/21562261-2848124

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