This work establishes a condition that determines when strong generation in the bounded
derived category of a Noetherian J-2 scheme is preserved by the derived pushforward of a …

Our work investigates a form of descent, in the fppf and h topologies, for generation of
triangulated categories obtained from noncommutative coherent algebras over schemes. In …

This work demonstrates classical generation is preserved by the derived pushforward along
the canonical morphism of a noncommutative scheme to its underlying scheme. There are …

This work explores bounds on the Rouquier dimension in the bounded derived category of
coherent sheaves on Noetherian schemes. By utilizing approximations, we exhibit that …

This work is concerned with approximability (\{a} la Neeman) and Rouquier dimension for
triangulated categories associated to noncommutative algebras over schemes. Amongst …

This work exhibits that the essential image of the derived pushforward along a proper
surjective morphism of Noetherian schemes generates the targets derived category of …

This work is concerned with a relationship regarding the closedness of the singular locus of
a Noetherian scheme and existence of classical generators in its category of coherent …

This work presents a range of triangulated characterizations for important classes of
singularities such as derived splinters, rational singularities, and Du Bois singularities. We …

This short note establishes derived characterizations for notions of rational pairs\{a} la
Schwede-Takagi and Koll\'{a} r-Kov\'{a} cs. We use a concept of generation in triangulated …

This work concerns maps of commutative noetherian local rings containing a field of positive
characteristic. Given such a map $\varphi $ of finite flat dimension, the results relate …