Abstract
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 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 P 3 \mathbb {P}^3 in a ‘purely characteristic- p p ’ configuration of points and lines.
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