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On the Geometric Subgroups of the Étale Fundamental Groups of Varieties over Real Closed Fields

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Abstract

In the present paper, we establish a “group-theoretic” algorithm for reconstructing, from the étale fundamental group of a suitable proper normal variety over a real closed field, the geometric subgroup of the étale fundamental group of the proper normal variety.

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References

  1. Barth, W., Peters, C., and Van de Ven, A.: Compact complex surfaces. Ergebnisse der Mathematik und ihrer Grenzgebiete (3), vol. 4. Springer, Berlin (1984)

  2. Mochizuki, S.: Topics in absolute anabelian geometry I: generalities. J. Math. Sci. Univ. Tokyo 19(2), 139–242 (2012)

    MathSciNet  MATH  Google Scholar 

  3. Ribes, L., Zalesskii, P.: Profinite groups. Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge. A Series of Modern Surveys in Mathematics, vol. 40. Springer, Berlin (2000)

  4. Stillwell, J.: Classical topology and combinatorial group theory. Graduate Texts in Mathematics, 2nd edn., vol. 72. Springer, New York (1993)

  5. Revêtements étales et groupe fondamental (SGA 1): Séminaire de géométrie algébrique du Bois Marie 1960-61. Directed by A. Grothendieck. With two papers by M. Raynaud. Updated and annotated reprint of the 1971 original. Documents Mathématiques (Paris), vol. 3. Société Mathématique de France, Paris (2003)

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Acknowledgements

The first author was supported by JSPS KAKENHI Grant Number 18K03239. The second author was supported by JSPS KAKENHI Grant Number 19J10214. The third author was supported by JSPS KAKENHI Grant Number 18J10260. This research was supported by the Research Institute for Mathematical Sciences, an International Joint Usage/Research Center located in Kyoto University.

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Authors and Affiliations

  1. Research Institute for Mathematical Sciences, Kyoto University, Kyoto, 606-8502, Japan

    Yuichiro Hoshi, Takahiro Murotani & Shota Tsujimura

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  1. Yuichiro Hoshi
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  2. Takahiro Murotani
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  3. Shota Tsujimura
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Correspondence to Shota Tsujimura.

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Hoshi, Y., Murotani, T. & Tsujimura, S. On the Geometric Subgroups of the Étale Fundamental Groups of Varieties over Real Closed Fields. Math. Z. 298, 215–229 (2021). https://doi.org/10.1007/s00209-020-02593-7

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  • DOI: https://doi.org/10.1007/s00209-020-02593-7

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