2024/08/06 by Küng, Felix
#13D09 #14A22 #18G80 #Algebraic Geometry (math.AG) #Category Theory (math.CT) #Commutative Algebra (math.AC) #FOS: Mathematics
paper · doi:10.48550/arxiv.2408.03027
We use injectives as a big tilting object to obstruct liftability of exact functors to the \dg-level. We use the inclusion of injectives into the canonical heart as a replacement for tilting objects in computations of the characteristic morphism. Then we apply this construction to proofs of non-liftability of candidate non-Fourier-Mukai functors, i.e. functors that do not admit an \Ainfty/\dg-lift. This approach allows explicit computation of the obstruction against an \Ainfty-lift. We in particular observe that this computation gives for smooth degree d>2 hypersurfaces an abundance of non-Fourier-Mukai functors.