Mod pq Galois representations and Serre's conjecture
| dc.creator | Khare, Chandrashekhar | |
| dc.creator | Kiming, Ian | |
| dc.date | 2002-10-25 | |
| dc.date.accessioned | 2026-07-07T04:52:22Z | |
| dc.date.available | 2026-07-07T04:52:22Z | |
| dc.description | Motives and automorphic forms of arithmetic type give rise to Galois representations that occur in {\it compatible families}. These compatible families are of p-adic representations with p varying. By reducing such a family mod p one obtains compatible families of mod p representations. While the representations that occur in such a p-adic or mod p family are strongly correlated, in a sense each member of the family reveals a new face of the motive. In recent celebrated work of Wiles playing off a pair of Galois representations in different characteristics has been crucial. In this paper we investigate when a pair of mod p and mod q representations of the absolute Galois group of a number field K simultaneously arises from an {\it automorphic motive}: we do this in the 1-dimensional (Section 2) and 2-dimensional (Section 3: this time assuming $K={\mathbb Q}$) cases. In Section 3 we formulate a mod pq version of Serre's conjecture refining in part a question of Barry Mazur and Ken Ribet. | |
| dc.description | This is an older preprint that was made available elsewhere on Sep. 19, 2001 | |
| dc.identifier | https://arxiv.org/abs/math/0210404 | |
| dc.identifier | http://arxiv.org/abs/math/0210404 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/65439 | |
| dc.subject | Number Theory | |
| dc.subject | 11R; 11F | |
| dc.title | Mod pq Galois representations and Serre's conjecture | |
| dc.type | text |