Geodesic
Monodromy for Some Rank Two Galois Representations over CM Fields
Documenta mathematica, Tome 25 (2020), pp. 2487-2506.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

We investigate local-global compatibility for cuspidal automorphic representations $\pi$ for $\operatorname{GL}_2$ over CM fields that are regular algebraic of weight $0$. We prove that for a Dirichlet density one set of primes $l$ and any $\iota : \overline{\mathbf{Q}}_l \xrightarrow {\sim} \mathbf{C}$, the $l$-adic Galois representation attached to $\pi$ and $\iota$ has nontrivial monodromy at any $v\nmid l$ in $F$ at which $\pi$ is special.
Classification : 11F80, 11R39
Keywords: Galois representations, automorphic forms, local-global compatibility, monodromy operator 
@article{DOCMA_2020__25__a2,
     author = {Allen, Patrick B. and Newton, James},
     title = {Monodromy for {Some} {Rank} {Two} {Galois} {Representations} over {CM} {Fields}},
     journal = {Documenta mathematica},
     pages = {2487--2506},
     publisher = {mathdoc},
     volume = {25},
     year = {2020},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DOCMA_2020__25__a2/}
}
TY  - JOUR
AU  - Allen, Patrick B.
AU  - Newton, James
TI  - Monodromy for Some Rank Two Galois Representations over CM Fields
JO  - Documenta mathematica
PY  - 2020
SP  - 2487
EP  - 2506
VL  - 25
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DOCMA_2020__25__a2/
LA  - en
ID  - DOCMA_2020__25__a2
ER  - 
%0 Journal Article
%A Allen, Patrick B.
%A Newton, James
%T Monodromy for Some Rank Two Galois Representations over CM Fields
%J Documenta mathematica
%D 2020
%P 2487-2506
%V 25
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DOCMA_2020__25__a2/
%G en
%F DOCMA_2020__25__a2
Allen, Patrick B.; Newton, James. Monodromy for Some Rank Two Galois Representations over CM Fields. Documenta mathematica, Tome 25 (2020), pp. 2487-2506. http://geodesic.mathdoc.fr/item/DOCMA_2020__25__a2/