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Linking complex analytic to nonstandard algebraic geometry

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Abstract

In this paper, we sketch some constructions providing a link between complex-analytic geometry and nonstandard algebraic geometry via a categorical point of view. The analytic category is seen as a completed fiber of a family of nonstandard algebraic geometries by applying a standard part functor. We indicate how various notions of analytic objects fit into this context (as for example banachanalytic spaces, Kähler spaces etc.)

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Acknowledgements

We thank the referees for insightful comments which led to significant improvements in the paper. Also, the first author would like to acknowledge the support provided by the Deanship of Scientific Research (DSR) at the King Fahd University of Petroleum and Minerals (KFUPM) for funding this work through Project No. IN161056.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, King Fahd University of Petroleum and Minerals, Dhahran, 31261, Saudi Arabia

    Adel Khalfallah

  2. Institut Fourier, Université Grenoble Alpes, 38402, St. Martin d’Hères, France

    Siegmund Kosarew

Authors
  1. Adel Khalfallah
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  2. Siegmund Kosarew
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Correspondence to Adel Khalfallah.

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Communicated by Bernd Siebert.

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Khalfallah, A., Kosarew, S. Linking complex analytic to nonstandard algebraic geometry. Abh. Math. Semin. Univ. Hambg. 90, 1–15 (2020). https://doi.org/10.1007/s12188-020-00216-w

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  • DOI: https://doi.org/10.1007/s12188-020-00216-w

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