Local epsilon isomorphisms
Number Theory
2015-11-03 v1
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.
Cite
@article{arxiv.1303.1785,
title = {Local epsilon isomorphisms},
author = {David Loeffler and Sarah Livia Zerbes and Otmar Venjakob},
journal= {arXiv preprint arXiv:1303.1785},
year = {2015}
}