Abstract
Let (X,F) be a pair of a smooth variety X over an algebraically closed field k of characteristic p>0 and its Frobenius morphism F. Given a Frobenius Wn(k)-lifting (X¯,F¯) of the pair (X,F) for n≥1, Nori and Srinivas [9] determined the obstruction obsX¯,F¯∈Ext(ΩX/k1,BF⁎ΩX/k1) to Frobenius Wn+1(k)-lifting of (X¯,F¯) in terms of Čech cohomology. The extension representing obsX¯,F¯ has been only known for n=1, which uses the Cartier operator. In this paper, we interpret obsX¯,F¯ in terms of Kato's version of de Rham-Witt Cartier operator [8] and determine the extension representing obsX¯,F¯ for n≥2.
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