Loeffler, D;
Zerbes, SL;
(2014)
Iwasawa theory and p-adic L-functions over Z(p)(2)-extensions.
International Journal of Number Theory
, 10
(8)
pp. 2045-2095.
10.1142/S1793042114500699.
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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 ℚp, 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 localization 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.
| Type: | Article |
|---|---|
| Title: | Iwasawa theory and p-adic L-functions over Z(p)(2)-extensions |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1142/S1793042114500699 |
| Publisher version: | https://doi.org/10.1142/S1793042114500699 |
| Language: | English |
| Additional information: | This version is the author accepted manuscript. For information on re-use, please refer to the publisher’s terms and conditions. |
| Keywords: | Iwasawa theoryp-adic regulatorp-adic L-function |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences |
| URI: | https://discovery.ucl.ac.uk/id/eprint/10088876 |
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