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ON THE TEMPERED FUNDAMENTAL GROUPS OF HYPERBOLIC CURVES OF GENUS $0$ OVER $\overline {\mathbb {Q}}_p$

Part of: Curves

Published online by Cambridge University Press:  01 June 2022

Shota Tsujimura Open the ORCID record for Shota Tsujimura [Opens in a new window]
Shota Tsujimura*
Affiliation:
Research Institute for Mathematical Sciences, Kyoto University, Kyoto 606-8502, Japan
*
stsuji@kurims.kyoto-u.ac.jp
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Abstract

Let p be a prime number. In the present paper, we prove that the moduli of hyperbolic curves of genus $0$ over an algebraic closure of the field of p-adic numbers may be completely determined by their tempered fundamental groups.

Keywords

anabelian geometryhyperbolic curvegenus 0tempered fundamental groupGrothendieck Conjecture

MSC classification

Primary: 14H30: Coverings, fundamental group
Type
Research Article
Information
Journal of the Institute of Mathematics of Jussieu , Volume 22 , Issue 6 , November 2023 , pp. 2833 - 2856
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Copyright
© The Author(s), 2022. Published by Cambridge University Press

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