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ID 56017
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Author
Minamide, Arata Research Institute for Mathematical Sciences Kyoto University
Abstract
In this paper, we prove that the etale fundamental group of a hyperbolic curve over an arithmetic field [e.g., a finite extension field of Q or Qp] or an algebraically closed field is indecomposable [i.e., cannot be decomposed into the direct product of nontrivial profinite groups]. Moreover, in the case of characteristic zero, we also prove that the etale fundamental group of the configuration space of a curve of the above type is indecomposable. Finally, we consider the topic of indecomposability in the context of the comparison of the absolute Galois group of Q with the Grothendieck-Teichmuller group GT and pose the question: Is GT indecomposable? We give an affirmative answer to a pro-l version of this question
Keywords
indecomposability
etale fundamental group
hyperbolic curve
con guration space
Grothendieck-Teichmuller group
Note
Mathematics Subject Classi cation. Primary 14H30; Secondary 11R99.
Published Date
2018-01
Publication Title
Mathematical Journal of Okayama University
Volume
volume60
Issue
issue1
Publisher
Department of Mathematics, Faculty of Science, Okayama University
Start Page
175
End Page
208
ISSN
0030-1566
NCID
AA00723502
Content Type
Journal Article
Official Url
http://www.math.okayama-u.ac.jp/mjou/
language
英語
Copyright Holders
Copyright©2018 by the Editorial Board of Mathematical Journal of Okayama University
File Version
publisher
Refereed
True
Submission Path
mjou/vol59/iss1/10