# The Galois representation arising from P1 − {0,1, ∞} and Tate twists of even degree

• Yasutaka Ihara
Conference paper
Part of the Mathematical Sciences Research Institute Publications book series (MSRI, volume 16)

## Abstract

The canonical representation
$${{\varphi }_{\mathbb{Q}}}:{{G}_{\mathbb{Q}}} = Gal(\bar{\mathbb{Q}}/\mathbb{Q}) \to Out {{\pi }_{1}}$$
of the absolute Galois group over the rationals in the outer automorphism group of the pro-ℓ fundamental group
$$_{\varphi Q}:{G_Q} = Gal\left( {\overline Q /Q} \right) \to Out\,\,{\pi _1}$$
(ℓ: a prime number) gives rise to an infinite sequence of solvable Galois extensions
$$\mathbb{Q}\, \subset \,\mathbb{Q}({\mu _{\ell \infty }})\, = \,\mathbb{Q}(1) \subset \, \cdots \subset \,\mathbb{Q}(m)\, \subset \mathbb{Q}(m + 1) \subset \cdots$$
over ℚ, unramified outside ℓ, satisfying the following properties [6,8].

## Keywords

Galois Representation Galois Extension Abelian Extension Absolute Galois Group Outer Automorphism Group
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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