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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

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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
Subjects: Q Science > QA Mathematics
Divisions: Faculty of Science, Engineering and Medicine > 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
Dates:
DateEvent
18 August 2021Published
15 July 2021Accepted
Volume: 27
Article Number: 82
DOI: 10.1007/s00029-021-00693-8
Status: Peer Reviewed
Publication Status: Published
Reuse Statement (publisher, data, author rights): 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
RIOXX Funder/Project Grant:
Project/Grant IDRIOXX Funder NameFunder ID
EP/T001615/1[EPSRC] Engineering and Physical Sciences Research Councilhttp://dx.doi.org/10.13039/501100000266
77180007Agencia Nacional de Investigación y DesarrolloUNSPECIFIED
11201025Agencia Nacional de Investigación y DesarrolloUNSPECIFIED
682152H2020 European Research Councilhttp://dx.doi.org/10.13039/100010663
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