2017/10/03 by Ballard, Matthew R., Diemer, Colin, Favero, David · 2 citations
#Algebraic Geometry (math.AG) #FOS: Mathematics
paper · doi:10.48550/arxiv.1710.01418
To any affine scheme with a \mathbbGm-action, we provide a Bousfield colocalization on the equivariant derived category of modules by constructing, via homotopical methods, an idempotent integral kernel. This endows the equivariant derived category with a canonical semi-orthogonal decomposition. As a special case, we demonstrate that grade-restriction windows appear as a consequence of this construction, giving a new proof of wall-crossing equivalences which works over an arbitrary base. The construction globalizes to yield interesting integral transforms associated to D-flips.