Replacing symmetric powers by divided powers and working over Witt vectors instead of ground fields, I generalize Kawamatas T -lifting theorem to characteristic p > 0. Combined with the work of Deligne–Illusie on degeneration of the Hodge–de Rham spectral sequences, this gives unobstructedness for certain Calabi–Yau varieties with free crystalline cohomology modules.

Replacing symmetric powers by divided powers and working over Witt vectors instead of ground fields, I generalize Kawamata’s T -lifting theorem to characteristic p > 0. Combined with the work of Deligne–Illusie on degeneration of the Hodge–de Rham spectral sequences, this gives unobstructedness for certain Calabi–Yau varieties with free crystalline cohomology modules.

In this note, we investigate the relationship between almost projective modules and generalized modules. These concepts are useful for study on finite direct sum of lifting It is proved that; if M N-projective any N, then N-projective. We also show that N lifting, im-small discuss question when again lifting.

Finitely-hollow lifting and hollow-weak modules are two generalizations of hollow module which is a weaker version module. In this paper, we have defined another generalization hollow-lifting namely finitely-hollow-weak (f-hollow-weak lifting) Various properties been seen found that, it not closed under quotients summands in general, so sufficient conditions provided f-hollow-weak property inhe...

Let B=A?X|dX=t? be an extended DG algebra by the adjunction of a variable positive even degree n, and let N semi-free B-module that is assumed to bounded below as graded module. We prove in this paper liftable A if ExtBn+1(N,N)=0. Furthermore such lifting unique up isomorphisms ExtBn(N,N)=0.