TY - JOUR
T1 - On the images of Galois representations attached to low weight Siegel modular forms
AU - Weiss, Ariel
N1 - Funding Information:
I would like to thank my PhD supervisor Tobias Berger for suggesting this problem, and for his constant help, guidance and support throughout my PhD. I am also grateful to Luis Dieulefait for a helpful discussion, which helped to shape the direction of the paper, and to Neil Dummigan and Toby Gee for their valuable feedback on my PhD thesis. Thanks also to Adel Betina, Andrea Conti, Frazer Jarvis, Jayanta Manoharmayum, Mohamed Moakher, Vincent Pilloni, Ciaran Schembri, Haluk Şengün, Benoît Stroh and Jacques Tilouine for helpful conversations, correspondences and feedback. Lastly, I would like to thank the anonymous referee for the helpful (and timely) comments and corrections they made for the final version of this paper.
Publisher Copyright:
© 2022 The Authors. Journal of the London Mathematical Society is copyright © London Mathematical Society.
PY - 2022/7/1
Y1 - 2022/7/1
N2 - Let (Formula presented.) be a cuspidal automorphic representation of (Formula presented.), whose archimedean component is a holomorphic discrete series or limit of discrete series representation. If (Formula presented.) is not CAP or endoscopic, then we show that its associated (Formula presented.) -adic Galois representations are irreducible and crystalline for (Formula presented.) of primes (Formula presented.). If, moreover, (Formula presented.) is neither an automorphic induction nor a symmetric cube lift, then we show that, for (Formula presented.) of primes (Formula presented.), the image of its mod (Formula presented.) Galois representation contains (Formula presented.).
AB - Let (Formula presented.) be a cuspidal automorphic representation of (Formula presented.), whose archimedean component is a holomorphic discrete series or limit of discrete series representation. If (Formula presented.) is not CAP or endoscopic, then we show that its associated (Formula presented.) -adic Galois representations are irreducible and crystalline for (Formula presented.) of primes (Formula presented.). If, moreover, (Formula presented.) is neither an automorphic induction nor a symmetric cube lift, then we show that, for (Formula presented.) of primes (Formula presented.), the image of its mod (Formula presented.) Galois representation contains (Formula presented.).
UR - http://www.scopus.com/inward/record.url?scp=85127775717&partnerID=8YFLogxK
U2 - 10.1112/jlms.12576
DO - 10.1112/jlms.12576
M3 - Article
AN - SCOPUS:85127775717
SN - 0024-6107
VL - 106
SP - 358
EP - 387
JO - Journal of the London Mathematical Society
JF - Journal of the London Mathematical Society
IS - 1
ER -