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Non-archimedean pinchings

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Abstract

We develop the theory of pinchings for non-archimedean analytic spaces. In particular, we show that although pinchings of affinoid spaces do not have to be affinoid, pinchings of Hausdorff analytic spaces always exist in the category of analytic spaces.

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References

  1. Vladimir, G.: Berkovich, Spectral theory and analytic geometry over non-Archimedean fields, Mathematical Surveys and Monographs, vol. 33. American Mathematical Society, Providence (1990)

    Google Scholar 

  2. Berkovich, Vladimir G.: Étale cohomology for non-Archimedean analytic spaces. Inst. Hautes Études Sci. Publ. Math. 1993(78), 5–161 (1994)

    MATH  Google Scholar 

  3. Bosch, S., Güntzer, U., Remmert, R.: Non-Archimedean analysis, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 261, Springer-Verlag, Berlin, 1984, A systematic approach to rigid analytic geometry

  4. Conrad, B., Temkin, M.: Descent for nonarchimedean analytic spaces. Tunis. J. Math. 3(4), 689–748 (2021)

    Article  MathSciNet  Google Scholar 

  5. Ducros, Antoine.: Families of Berkovich spaces. Astérisque, no. 400, vii+262 (2018)

  6. Ferrand, Daniel: Conducteur, descente et pincement. Bull. Soc. Math. France 131(4), 553–585 (2003)

    Article  MathSciNet  Google Scholar 

  7. Liu, Q.: Un contre-exemple au “critère cohomologique d’affinoïdicité’’. C. R. Acad. Sci. Paris Sér. I Math. 307(2), 83–86 (1988)

    MathSciNet  MATH  Google Scholar 

  8. Liu, Q.: Sur les espaces de Stein quasi-compacts en géométrie rigide. Tohoku Math. J. 42(3), 289–306 (1990)

    Article  MathSciNet  Google Scholar 

  9. Maculan, Marco, Poineau, Jérôme.: Notions of Stein spaces in non-archimedean geometry. J. Algebraic Geom. 30(2), 287–330 (2021)

    Article  MathSciNet  Google Scholar 

  10. Poineau, Jérôme.: Les espaces de Berkovich sont angéliques. Bull. Soc. Math. France 141(2), 267–297 (2013)

    Article  MathSciNet  Google Scholar 

  11. Porta, Mauro, Yu, Tony Yue: Representability theorem in derived analytic geometry. J. Eur. Math. Soc. (JEMS) 22(12), 3867–3951 (2020)

    Article  MathSciNet  Google Scholar 

  12. The Stacks Project Authors, Stacks Project, http://stacks.math.columbia.edu

  13. On local properties of non-Archimedean analytic spaces II.: Temkin, Michael. Israel J. Math. 140, 1–27 (2004)

  14. Temkin, Michael, Tyomkin, Ilya: Ferrand pushouts for algebraic spaces. Eur. J. Math. 2(4), 960–983 (2016)

    Article  MathSciNet  Google Scholar 

  15. Xia, M.: On Liu morphisms in non-archimedean geometry. (2021), arXiv:2106.08032

Download references

Acknowledgements

The author is grateful to Jérôme Poineau, Antoine Ducros and Tony Yu Yue for useful discussions. Also, he is very grateful for the referee for careful reading of the first version of the paper and pointing out various inaccuracies.

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  1. Einstein Institute of Mathematics, The Hebrew University of Jerusalem, Edmond J. Safra Campus, Giv’at Ram, Jerusalem, 91904, Israel

    Michael Temkin

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  1. Michael Temkin
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Correspondence to Michael Temkin.

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This research is supported by ERC Consolidator Grant 770922 - BirNonArchGeom.

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Temkin, M. Non-archimedean pinchings. Math. Z. 301, 2099–2109 (2022). https://doi.org/10.1007/s00209-022-02979-9

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  • DOI: https://doi.org/10.1007/s00209-022-02979-9

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