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Some geometric results on K-theory with \({\mathbb{Z}}/k{\mathbb{Z}}\)-coefficients

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Abstract

We establish some geometric results on K-theory with coefficients in \({\mathbb{Z}}/k{\mathbb{Z}}\). The first one is a new proof of the Atiyah–Patodi–Singer mod k index theorem (Math Proc Camb Philos Soc 79:71–99, 1976) in the case of Dirac operators, i.e. in a geometric situation. The second one is a Grothendieck–Riemann–Roch theorem for \({\mathbb{Z}}/k{\mathbb{Z}}\)-K-theory.

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Acknowledgements

The author is grateful to the referees for valuable comments and suggestions

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Authors and Affiliations

  1. Department of Mathematics, Ibn Tofaïl University, Kenitra, Morocco

    Adnane Elmrabty

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  1. Adnane Elmrabty
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Correspondence to Adnane Elmrabty.

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Communicated by Ugo Bruzzo.

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Elmrabty, A. Some geometric results on K-theory with \({\mathbb{Z}}/k{\mathbb{Z}}\)-coefficients. São Paulo J. Math. Sci. 14, 562–579 (2020). https://doi.org/10.1007/s40863-020-00179-z

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