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Iwasawa theory and p-adic L-functions over Zp2-extensions
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Loeffler, David and Zerbes, Sarah Livia (2014) Iwasawa theory and p-adic L-functions over Zp2-extensions. International Journal of Number Theory, 10 (8). pp. 2045-2095. doi:10.1142/S1793042114500699 ISSN 1793-0421.
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Official URL: http://dx.doi.org/10.1142/S1793042114500699
Abstract
We construct a two-variable analogue of Perrin-Riou’s p-adic regulator map for the Iwasawa cohomology of a crystalline representation of the absolute Galois group of Q p , over a Galois extension whose Galois group is an abelian p-adic Lie group of dimension 2. We use this regulator map to study p-adic representations of global Galois groups over certain abelian extensions of number fields whose localisation at the primes above p is an extension of the above type. In the example of the restriction to an imaginary quadratic field of the representation attached to a modular form, we formulate a conjecture on the existence of a “zeta element”, whose image under the regulator map is a p-adic L-function. We show that this conjecture implies the known properties of the 2-variable p-adic L-functions constructed by Perrin-Riou and Kim.
Item Type: | Journal Article | ||||||||
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Subjects: | Q Science > QA Mathematics | ||||||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||||||
Library of Congress Subject Headings (LCSH): | L-functions, p-adic analysis | ||||||||
Journal or Publication Title: | International Journal of Number Theory | ||||||||
Publisher: | World Scientific Publishing Co. Pte. Ltd. | ||||||||
ISSN: | 1793-0421 | ||||||||
Official Date: | 5 May 2014 | ||||||||
Dates: |
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Volume: | 10 | ||||||||
Number: | 8 | ||||||||
Number of Pages: | 45 | ||||||||
Page Range: | pp. 2045-2095 | ||||||||
DOI: | 10.1142/S1793042114500699 | ||||||||
Status: | Peer Reviewed | ||||||||
Publication Status: | Published | ||||||||
Access rights to Published version: | Open Access (Creative Commons) | ||||||||
Date of first compliant deposit: | 27 January 2016 | ||||||||
Date of first compliant Open Access: | 27 January 2016 | ||||||||
Funder: | Royal Society (Great Britain), Engineering and Physical Sciences Research Council (EPSRC) | ||||||||
Grant number: | EP/J018716/1 (EPSRC) | ||||||||
Open Access Version: |
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