Families of Bianchi modular symbols: critical base-change p-adic L-functions and p-adic Artin formalism

• Daniel Barrera Salazar ^[1] ; Chris Williams ^[2]
  1. [1] Universidad de Santiago de Chile

     Universidad de Santiago de Chile

     Santiago, Chile

     
  2. [2] University of Warwick

     University of Warwick

     Reino Unido

     
• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 27, Nº. 5, 2021
• Idioma: inglés
• DOI: 10.1007/s00029-021-00693-8
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• Resumen

  • 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.