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Mathematische Zeitschrift

, Volume 288, Issue 3–4, pp 1103–1142 | Cite as

Tannakian duality over Dedekind rings and applications

  • Nguyen Dai Duong
  • Phùng Hô Hai
Article

Abstract

We establish a duality between flat affine group schemes and rigid tensor categories equipped with a neutral fiber functor (called Tannakian lattice), both defined over a Dedekind ring. We use this duality and the known Tannakian duality due to Saavedra to study morphisms between flat affine group schemes. Next, we apply our new duality to the category of stratified sheaves on a smooth scheme over a Dedekind ring R to define the relative differential fundamental group scheme of the given scheme and compare the fibers of this group scheme with the fundamental group scheme of the fibers. When R is a complete DVR of equal characteristic we show that this category is Tannakian in the sense of Saavedra.

Mathematics Subject Classification

14L17 14F10 

Notes

Acknowledgements

The second named author would like to thank H. Esnault and J.P. dos Santos for their interests in the work and very helpful discussions. He would also like to express his gratitude to J.-P. Serre for explaining him about flat coalgebras.

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Copyright information

© Springer-Verlag GmbH Deutschland 2017

Authors and Affiliations

  1. 1.Institute of MathematicsVietnam Academy of Science and TechnologyHanoiVietnam

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