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Mod pq Galois representations and Serre's conjecture
- Source :
- Journal of Number Theory. 98(2):329-347
- Publication Year :
- 2003
- Publisher :
- Elsevier BV, 2003.
-
Abstract
- 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.<br />This is an older preprint that was made available elsewhere on Sep. 19, 2001
- Subjects :
- Discrete mathematics
11R
11F
Pure mathematics
Algebra and Number Theory
Mathematics - Number Theory
Galois cohomology
Fundamental theorem of Galois theory
Mathematics::Number Theory
Galois group
Abelian extension
Galois module
Differential Galois theory
Embedding problem
symbols.namesake
symbols
FOS: Mathematics
Galois extension
Number Theory (math.NT)
Mathematics
Subjects
Details
- ISSN :
- 0022314X
- Volume :
- 98
- Issue :
- 2
- Database :
- OpenAIRE
- Journal :
- Journal of Number Theory
- Accession number :
- edsair.doi.dedup.....2c26fbd3f04942f3b61487377bae46d8
- Full Text :
- https://doi.org/10.1016/s0022-314x(02)00043-4