5 papers
Nonexistence of singly compactly generated -structures for schemes
Anirban Bhaduri, Timothy De Deyn, Michal Hrbek +2
We show the first instances of schemes whose standard aisles on their derived category of quasi-coherent sheaves are not singly compactly generated.
Simple criteria for higher rational singularities
Sándor Kovács, Pat Lank, Sridhar Venkatesh
This work establishes simple criteria for detecting higher rational singularities via the intersection Du Bois complex and the irrationality complex of a normal variety over the co…
Compact approximation and descent for algebraic stacks
Jack Hall, Alicia Lamarche, Pat Lank +1
This work focuses on approximation and generation for the derived category of complexes with quasi-coherent cohomology on algebraic stacks. Our methods establish that approximation…
Descending strong generation in algebraic geometry
Timothy De Deyn, Pat Lank, Kabeer Manali Rahul
We formalize the main approach for showing Zariski descent-type statements for strong generation of triangulated categories associated to algebro-geometric objects. This recovers v…
Integral transforms on singularity categories for Noetherian schemes
Uttaran Dutta, Pat Lank, Kabeer Manali Rahul
This work studies conditions under which integral transforms induce exact functors on singularity categories between schemes that are proper over a Noetherian base scheme. A comple…