Reference : Big images of two-dimensional pseudo representations |

E-prints/Working papers : Already available on another site | |||

Physical, chemical, mathematical & earth Sciences : Mathematics | |||

http://hdl.handle.net/10993/41381 | |||

Big images of two-dimensional pseudo representations | |

English | |

Conti, Andrea [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit >] | |

Lang, Jaclyn [Université Paris 13 > Mathematics > LAGA > Postdoctorante] | |

Medvedovsky, Anna [Boston University > Mathematics] | |

Apr-2019 | |

No | |

[en] For an odd prime p, we study the image of a continuous 2-dimensional (pseudo)representation rho of a profi nite group with coe cients in a local pro-p domain A. Under mild conditions, Bella che has proved that the image of rho contains a nontrivial congruence subgroup of SL2(B) for a certain subring B
of A. We prove that the ring B can be slightly enlarged and then described in terms of the conjugate self-twists of rho, symmetries that naturally constrain its image; hence this new B is optimal. We use this result to recover, and in some cases improve, the known large-image results for Galois representations arising from elliptic and Hilbert modular forms due to Serre, Ribet and Momose, and Nekov a r, and p-adic Hida or Coleman families of elliptic modular forms due to Hida, Lang, and Conti-Iovita-Tilouine. | |

http://hdl.handle.net/10993/41381 | |

https://arxiv.org/abs/1904.10519 |

File(s) associated to this reference | ||||||||||||||

| ||||||||||||||

All documents in ORBi^{lu} are protected by a user license.