Geodesic
Monodromy for Some Rank Two Galois Representations over CM Fields
Documenta mathematica, Tome 25 (2020), pp. 2487-2506
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We investigate local-global compatibility for cuspidal automorphic representations π for GL2​ over CM fields that are regular algebraic of weight 0. We prove that for a Dirichlet density one set of primes l and any ι:Q​l​∼​C, the l-adic Galois representation attached to π and ι has nontrivial monodromy at any v∤l in F at which π is special.
DOI : 10.4171/dm/805
Classification : 11F80, 11R39
Mots-clés : Galois representations, automorphic forms, local-global compatibility, monodromy operator 
@article{10_4171_dm_805,
     author = {Patrick B. Allen and James Newton},
     title = {Monodromy for {Some} {Rank} {Two} {Galois} {Representations} over {CM} {Fields}},
     journal = {Documenta mathematica},
     pages = {2487--2506},
     year = {2020},
     volume = {25},
     doi = {10.4171/dm/805},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/805/}
}
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Patrick B. Allen; James Newton. Monodromy for Some Rank Two Galois Representations over CM Fields. Documenta mathematica, Tome 25 (2020), pp. 2487-2506. doi: 10.4171/dm/805

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