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Families of Bianchi modular symbols : critical base-change p-adic L-functions and p-adic Artin formalism
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Barrera Salazar, Daniel and Williams, Christopher David (2021) Families of Bianchi modular symbols : critical base-change p-adic L-functions and p-adic Artin formalism. Selecta Mathematica, 27 . 82. doi:10.1007/s00029-021-00693-8
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Official URL: https://doi.org/10.1007/s00029-021-00693-8
Abstract
Let K be an imaginary quadratic field. In this article, we study the eigenvariety for GL2/K, proving an étaleness result for the weight map at non-critical classical points and a smoothness result at base-change classical points. We give three main applications of this; let f be a p-stabilised newform of weight k≥2 without CM by K. Suppose f has finite slope at p and its base-change f/K to K is p-regular. Then: (1) We construct a two-variable p-adic L-function attached to f/K under assumptions on f that conjecturally always hold, in particular with no non-critical assumption on f/K. (2) We construct three-variable p-adic L-functions over the eigenvariety interpolating the p-adic L-functions of classical base-change Bianchi cusp forms. (3) We prove that these base-change p-adic L-functions satisfy a p-adic Artin formalism result, that is, they factorise in the same way as the classical L-function under Artin formalism.
In an appendix, Carl Wang-Erickson describes a base-change deformation functor and gives a characterisation of its Zariski tangent space.
| Item Type: | Journal Article | |||||||||||||||
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| Subjects: | Q Science > QA Mathematics | |||||||||||||||
| Divisions: | Faculty of Science > Mathematics | |||||||||||||||
| Library of Congress Subject Headings (LCSH): | Forms, Modular, P-adic numbers, L-functions, Algebraic number theory | |||||||||||||||
| Journal or Publication Title: | Selecta Mathematica | |||||||||||||||
| Publisher: | Springer | |||||||||||||||
| ISSN: | 1022-1824 | |||||||||||||||
| Official Date: | 18 August 2021 | |||||||||||||||
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| Volume: | 27 | |||||||||||||||
| Article Number: | 82 | |||||||||||||||
| DOI: | 10.1007/s00029-021-00693-8 | |||||||||||||||
| Status: | Peer Reviewed | |||||||||||||||
| Publication Status: | Published | |||||||||||||||
| Publisher Statement: | This is a post-peer-review, pre-copyedit version of an article published in Selecta Mathematica. The final authenticated version is available online at: http://dx.doi.org/[insert DOI]”. | |||||||||||||||
| Access rights to Published version: | Open Access | |||||||||||||||
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