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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Some elementary examples of non-liftable varieties
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by Piotr Achinger and Maciej Zdanowicz PDF
Proc. Amer. Math. Soc. 145 (2017), 4717-4729 Request permission


We present some simple examples of smooth projective varieties in positive characteristic, arising from linear algebra, which do not admit a lifting neither to characteristic zero, nor to the ring of Witt vectors of length $2$. Our first construction is the blow-up of the graph of the Frobenius morphism of a homogeneous space. The second example is a blow-up of $\mathbb {P}^3$ in a ‘purely characteristic-$p$’ configuration of points and lines.
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Additional Information
  • Piotr Achinger
  • Affiliation: Banach Center, Instytut Matematyczny PAN, Śniadeckich 8, Warsaw, Poland
  • Email:
  • Maciej Zdanowicz
  • Affiliation: Wydział Matematyki, Informatyki i Mechaniki UW, Banacha 2, Warsaw, Poland
  • Email:
  • Received by editor(s): July 5, 2016
  • Received by editor(s) in revised form: December 9, 2016, and December 14, 2016
  • Published electronically: June 5, 2017
  • Additional Notes: The first author was supported by NCN OPUS grant number UMO-2015/17/B/ST1/02634
    The second author was supported by NCN PRELUDIUM grant number UMO-2014/13/N/ST1/02673. This work was partially supported by the grant 346300 for IMPAN from the Simons Foundation and the matching 2015–2019 Polish MNiSW fund
  • Communicated by: Lev Borisov
  • © Copyright 2017 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 145 (2017), 4717-4729
  • MSC (2010): Primary 14D15; Secondary 14G17
  • DOI:
  • MathSciNet review: 3691989