✦ LIBER ✦
On the Automorphism Group of a Free Pro-l Meta-abelian Group and an Application to Galois Representations
✍ Scribed by Hiroshi Tsunogai
- Publisher
- John Wiley and Sons
- Year
- 1995
- Tongue
- English
- Weight
- 431 KB
- Volume
- 171
- Category
- Article
- ISSN
- 0025-584X
No coin nor oath required. For personal study only.
✦ Synopsis
Abstract
In § l of this article, we study group‐theoretical properties of some automorphism group Ψ^*^ of the meta‐abelian quotient § of a free pro‐l group § of rank two, and show that the conjugacy class of some element of order two of Ψ^*^ is not determined by the action induced on the abelian quotient § of § in the case of § = 2. In § 2 we apply the results to the outer Galois representation § attached to the curve C deleted one point from an elliptic curve E, and give an example that §~c~ does not factor through the l‐adic representation attached to E.