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What clsses of algebraic varieties over field of positive characteristic can be lift to $W_2(k)$?

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Curves, K3 surfaces, abelian varieties, ... is there more context to the question or is this just a "big list"? – Matt Apr 10 '11 at 19:09
    
All affine varieties, trivially! are you assuming $k$ to be perfect? and is the motivation stemming from Deligne-Illusie's famous paper? – SGP Apr 10 '11 at 21:58
    
In addition to affine varieties, curves, K3 surfaces, abelian varieties, have anything else which statisfy the liftability? The $k$ may be perfect or even algebraically closed. – Universe Apr 11 '11 at 10:57
    
Is there a particular variety or class of varieties you want to be liftable? Perhaps that would give you a better answer. – Karl Schwede Apr 11 '11 at 11:15
    
I want to know as much as possible class of schemes or varieties(especially projective), which can be lift to $W_2(k)$. Does any toric varieties always liftable? – Universe Apr 11 '11 at 12:50

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