We study the motivic and ℓ-adic realizations of the dg category of singularities of the zero
locus of a global section of a line bundle over a regular scheme. We will then use the …

Let $ p: X\rightarrow S $ be a flat, proper and regular scheme over a strictly henselian
discrete valuation ring. We prove that the singularity category of the special fiber with its …

Let A be a ring (not necessarily commutative, but noetherian 1). Associated to A are many
interesting invariants, which tell us about the geometry, homological algebra, representation …

We provide an equivalence between the dg category of coherent matrix factorizations and a
certain dg category of absolute singularities. As an application, we compute the-adic …