Abstract
Abstract
Given any commutative Noetherian ring R and an element x in R, we consider the full subcategory
$\mathsf{C}(x)$
of its singularity category consisting of objects for which the morphism that is given by the multiplication by x is zero. Our main observation is that we can establish a relation between
$\mathsf{C}(x), \mathsf{C}(y)$
and
$\mathsf{C}(xy)$
for any two ring elements x and y. Utilizing this observation, we obtain a decomposition of the singularity category and consequently an upper bound on the dimension of the singularity category.
Publisher
Cambridge University Press (CUP)