ID | 56017 |
FullText URL | |
Author |
Minamide, Arata
Research Institute for Mathematical Sciences Kyoto University
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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
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Keywords | indecomposability
etale fundamental group
hyperbolic curve
conguration space
Grothendieck-Teichmuller group
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Note | Mathematics Subject Classication. Primary 14H30; Secondary 11R99.
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Published Date | 2018-01
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Publication Title |
Mathematical Journal of Okayama University
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Volume | volume60
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Issue | issue1
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Publisher | Department of Mathematics, Faculty of Science, Okayama University
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Start Page | 175
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End Page | 208
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ISSN | 0030-1566
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NCID | AA00723502
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Content Type |
Journal Article
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Official Url | http://www.math.okayama-u.ac.jp/mjou/
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language |
English
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Copyright Holders | Copyright©2018 by the Editorial Board of Mathematical Journal of Okayama University
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File Version | publisher
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Refereed |
True
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Submission Path | mjou/vol59/iss1/10
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