Mathematical Journal of Okayama University 60巻 1号
2018-01 発行

Indecomposability of various profinite groups arising from hyperbolic curves

Minamide, Arata Research Institute for Mathematical Sciences Kyoto University
Publication Date
2018-01
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
Comments
Mathematics Subject Classi cation. Primary 14H30; Secondary 11R99.
ISSN
0030-1566
NCID
AA00723502