Essential dimension of inifinitesimal commutative unipotent group schemes

Abstract

We propose a generalization of Ledet’s conjecture, which predicts the essential dimension of cyclic p-groups in characteristic p, for finite commutative unipotent group schemes. And we present some evidence for this conjecture and discuss some consequences.

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Notes

  1. 1.

    We remark that the proof of [1, Theorem 6.19], which we used before and which is the standard reference for this result, works only for affine group schemes since it uses versal torsors. We remark that in [1] an algebraic group is intended to be affine.

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Acknowledgements

I would like to thank A. Vistoli for useful comments and conversations. I also acknowledge the help of the referee to improve the exposition of this article. I have been partially supported by the project ANR-10-JCJC 0107 from the Agence Nationale de la Recherche. This work was partly elaborated during a stay at Max Planck Institute of Bonn.

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Correspondence to Dajano Tossici.

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Tossici, D. Essential dimension of inifinitesimal commutative unipotent group schemes. Boll Unione Mat Ital 12, 575–581 (2019). https://doi.org/10.1007/s40574-019-00192-x

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Keywords

  • Group schemes
  • Torsors
  • Essential dimension

Mathematics Subject Classification

  • 14L15
  • 14L30
  • 14F20