Mod pq Galois representations and Serre's conjecture

Details Mod pq Galois representations and Serre's conjecture Mod pq Galois representations and Serre's conjecture

2002-10-25

arxiv.org/abs/math/0210404v1

Mathematics

Number Theory

This is an older preprint that was made available elsewhere on Sep. 19, 2001

Scientific paper

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.

Affiliated with

Also associated with

No associations

Rating

Mod pq Galois representations and Serre's conjecture does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Mod pq Galois representations and Serre's conjecture, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Mod pq Galois representations and Serre's conjecture will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-614576