Kyoto Journal of Mathematics

Local epsilon isomorphisms

David Loeffler, Otmar Venjakob, and Sarah Livia Zerbes

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Abstract

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 Qp, 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 2-variable version of the Perrin-Riou regulator map constructed by the first and third authors.

Article information

Source
Kyoto J. Math., Volume 55, Number 1 (2015), 63-127.

Dates
First available in Project Euclid: 13 March 2015

Permanent link to this document
https://projecteuclid.org/euclid.kjm/1426252131

Digital Object Identifier
doi:10.1215/21562261-2848124

Mathematical Reviews number (MathSciNet)
MR3323528

Zentralblatt MATH identifier
1322.11112

Subjects
Primary: 11R23: Iwasawa theory
Secondary: 11S40: Zeta functions and $L$-functions [See also 11M41, 19F27]

Citation

Loeffler, David; Venjakob, Otmar; Zerbes, Sarah Livia. Local epsilon isomorphisms. Kyoto J. Math. 55 (2015), no. 1, 63--127. doi:10.1215/21562261-2848124. https://projecteuclid.org/euclid.kjm/1426252131


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