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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
収録刊行物
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- Mathematical Journal of Okayama University
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Mathematical Journal of Okayama University 60 (1), 175-208, 2018-01
Department of Mathematics, Faculty of Science, Okayama University
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詳細情報 詳細情報について
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- CRID
- 1390009224823270784
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- NII論文ID
- 120006489929
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- NII書誌ID
- AA00723502
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- ISSN
- 00301566
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- 本文言語コード
- en
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- JaLC
- IRDB
- CiNii Articles