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Annihilators and decompositions of singularity categories
- Part of
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- Journal:
- Proceedings of the Edinburgh Mathematical Society / Volume 67 / Issue 3 / August 2024
- Published online by Cambridge University Press:
- 23 April 2024, pp. 699-713
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- Article
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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.
