Monodromy for Some Rank Two Galois Representations over CM Fields

  • Patrick B. Allen

    Department of Mathematics and Statistics, McGill University, Montreal, Quebec H3A 0B9, Canada
  • James Newton

    Department of Mathematics, King's College London, London WC2R 2LS, UK
Monodromy for Some Rank Two Galois Representations over CM Fields cover
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Abstract

We investigate local-global compatibility for cuspidal automorphic representations π\pi for GL2\operatorname{GL}_2 over CM fields that are regular algebraic of weight 00. We prove that for a Dirichlet density one set of primes ll and any ι:QlC\iota : \overline{\mathbf{Q}}_l \xrightarrow {\sim} \mathbf{C}, the ll-adic Galois representation attached to π\pi and ι\iota has nontrivial monodromy at any vlv\nmid l in FF at which π\pi is special.

Cite this article

Patrick B. Allen, James Newton, Monodromy for Some Rank Two Galois Representations over CM Fields. Doc. Math. 25 (2020), pp. 2487–2506

DOI 10.4171/DM/805