Hiroshima Mathematical Journal

Galois action on mapping class groups

Yu Iijima

Full-text: Open access

Abstract

Let l be a prime number. In the paper, we study the outer Galois action on the profinite and the relative pro-l completions of mapping class groups of pointed orientable topological surfaces. In the profinite case, we prove that the outer Galois action is faithful. In the pro-l case, we prove that the kernel of the outer Galois action has certain stability properties with respect to the genus and the number of punctures. Also, we prove a variant of the above results for arbitrary families of curves.

Article information

Source
Hiroshima Math. J., Volume 45, Number 2 (2015), 207-230.

Dates
First available in Project Euclid: 10 August 2015

Permanent link to this document
https://projecteuclid.org/euclid.hmj/1439219709

Digital Object Identifier
doi:10.32917/hmj/1439219709

Mathematical Reviews number (MathSciNet)
MR3379003

Zentralblatt MATH identifier
06490133

Subjects
Primary: 14H30: Coverings, fundamental group [See also 14E20, 14F35]
Secondary: 14H10: Families, moduli (algebraic)

Keywords
Mapping class group outer Galois representation hyperbolic curve

Citation

Iijima, Yu. Galois action on mapping class groups. Hiroshima Math. J. 45 (2015), no. 2, 207--230. doi:10.32917/hmj/1439219709. https://projecteuclid.org/euclid.hmj/1439219709


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