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Finite tripod variants of I/OM

On Ihara’s question/Oda–Matsumoto conjecture
  • Florian PopEmail author
Article
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Abstract

In this note we introduce and prove a wide generalization and sharpening of Ihara’s question / Oda–Matsumoto conjecture, for short I/OM. That leads to a quite concrete topological/combinatorial description of absolute Galois groups, in particular of \(\mathrm{Gal}_{{\mathbb {Q}}}=\mathrm{Aut}(\overline{{\mathbb {Q}}})\), as envisioned by Grothendieck in his Esquisse d’ un Programme.

Mathematics Subject Classification

Primary 11G99 12F10 12G99 14A99 

Notes

Acknowledgements

I would like to thank Ching-Li Chai, Franz Oort, Jakob Stix, Alexander Schmidt and Tamás Szamuely for technical discussions and help, Pierre Lochak for insisting that these facts should be thoroughly investigated, and many others who showed interest in this work: Yves André, Pierre Deligne, R. Hain, Y. Ihara, Minhyong Kim, M. Matsumoto, N. Nakamura, M. Saidi, A. Tamagawa for discussions on several occasions. Special thanks are due to the University of Heidelberg, University of Bonn, and there MPI Bonn, for the excellent working conditions during my visits there as visiting scientist. Last but not least, many thanks to the referee, for the careful reading of the manuscript and suggestions to improve the presentation.

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of PennsylvaniaPhiladelphiaUSA

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