On the GLn-eigenvariety and a conjecture of Venkatesh

• David Hansen ^[1] ; Jack A. Thorne ^[2]
  1. [1] Columbia University

     Columbia University

     Estados Unidos

     
  2. [2] University of Cambridge

     University of Cambridge

     Cambridge District, Reino Unido

     
• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 23, Nº. 2, 2017, págs. 1205-1234
• Idioma: inglés
• DOI: 10.1007/s00029-017-0303-0
• Enlaces
  • Texto completo
• Resumen

  • Let π be a cuspidal, cohomological automorphic representation of GLn(A).

    Venkatesh has suggested that there should exist a natural action of the exterior algebra of a certain motivic cohomology group on the π-part of the Betti cohomology (with rational coefficients) of the GLn(Q)-arithmetic locally symmetric space. Venkatesh has given evidence for this conjecture by showing that its ‘l-adic realization’ is a consequence of the Taylor–Wiles formalism. We show that its ‘p-adic realization’ is related to the properties of eigenvarieties.