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Integral motives, relative Krull–Schmidt principle, and Maranda-type theorems

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In the present article we investigate properties of the category of integral Grothendieck-Chow motives over a field. We discuss the Krull–Schmidt principle for integral motives, provide a complete list of generalized Severi-Brauer varieties with indecomposable integral motive, and exploit a relation between the category of motives of twisted flag varieties and integral \(p\)-adic representations of finite groups.

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Acknowledgments

We would like to thank sincerely Skip Garibaldi and Esther Beneish for numerous e-mail conversations on the subject of the paper and for sharing with us their knowledge of algebraic groups and of integral representations of finite groups.

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Authors and Affiliations

  1. Institut für Mathematik, Johannes Gutenberg-Universität Mainz, Staudingerweg 9, 55128, Mainz, Germany

    Nikita Semenov & Maksim Zhykhovich

Authors
  1. Nikita Semenov
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  2. Maksim Zhykhovich
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Correspondence to Nikita Semenov.

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The authors gratefully acknowledge the support of the Sonderforschungsbereich/Transregio 45 “Periods, moduli spaces, and arithmetic of algebraic varieties” (Bonn-Essen-Mainz).

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Semenov, N., Zhykhovich, M. Integral motives, relative Krull–Schmidt principle, and Maranda-type theorems. Math. Ann. 363, 61–75 (2015). https://doi.org/10.1007/s00208-014-1158-8

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  • DOI: https://doi.org/10.1007/s00208-014-1158-8

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