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June 2004 On the Galois Actions on the Fundamental Group of $\mathbf{P}^1_{\mathbf{Q}(\mu_n)} \backslash \{0,\mu_n,\infty\}$
Jean-Claude DOUAI, Zdzislaw WOJTKOWIAK
Tokyo J. Math. 27(1): 21-34 (June 2004). DOI: 10.3836/tjm/1244208471

Abstract

We are studying the action of Galois groups on the pro-$l$ completion of the fundamental group of $\mathbf{P}^1_{\overline{\mathbf{Q}(\mu_n)}} \backslash \{0,\mu_n,\infty\}$. If $n=2p$, where $p$ is an odd prime number then the Lie algebra of derivations associated to the image of $\text{Gal}(\overline{\mathbf{Q}} / \mathbf{Q}(\mu_{2p\cdot l^\infty}))$ has $\frac{p-1}{2}$ generators in each even degree and $\frac{p-1}{2}$ generators in each odd degree greater than $1.$ We shall show that generators in even degrees generate a free Lie algebra.

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Jean-Claude DOUAI. Zdzislaw WOJTKOWIAK. "On the Galois Actions on the Fundamental Group of $\mathbf{P}^1_{\mathbf{Q}(\mu_n)} \backslash \{0,\mu_n,\infty\}$." Tokyo J. Math. 27 (1) 21 - 34, June 2004. https://doi.org/10.3836/tjm/1244208471

Information

Published: June 2004
First available in Project Euclid: 5 June 2009

zbMATH: 1169.14308
MathSciNet: MR2060071
Digital Object Identifier: 10.3836/tjm/1244208471

Rights: Copyright © 2004 Publication Committee for the Tokyo Journal of Mathematics

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Vol.27 • No. 1 • June 2004
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