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2007 A combinatorial version of the Grothendieck conjecture
Shinichi Mochizuki
Tohoku Math. J. (2) 59(3): 455-479 (2007). DOI: 10.2748/tmj/1192117988


We study the "combinatorial anabelian geometry" that governs the relationship between the dual semi-graph of a pointed stable curve and various associated profinite fundamental groups of the pointed stable curve. Although many results of this type have been obtained previously in various particular situations of interest under unnecessarily strong hypotheses, the goal of the present paper is to step back from such "typical situations of interest" and instead to consider this topic in the abstract -- a point of view which allows one to prove results of this type in much greater generality under very weak hypotheses.


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Shinichi Mochizuki. "A combinatorial version of the Grothendieck conjecture." Tohoku Math. J. (2) 59 (3) 455 - 479, 2007.


Published: 2007
First available in Project Euclid: 11 October 2007

zbMATH: 1129.14043
MathSciNet: MR2365351
Digital Object Identifier: 10.2748/tmj/1192117988

Primary: 14H30
Secondary: 14H25

Rights: Copyright © 2007 Tohoku University

Vol.59 • No. 3 • 2007
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