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)


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].


Galois Representation Galois Extension Abelian Extension Absolute Galois Group Outer Automorphism Group 
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Copyright information

© Springer-Verlag New York Inc. 1989

Authors and Affiliations

  • Yasutaka Ihara
    • 1
  1. 1.Department of Mathematics, Faculty of ScienceUniversity of TokyoTokyo 113Japan

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