27 papers
Dualizing complexes and -structures for algebraic spaces
Pat Lank
The paper proves the existence of dualizing complexes for suitable Deligne–Mumford stacks and uses this to classify all tensor t‑structures on the bounded derived category of coher…
Perfect generation for regular algebraic stacks
Pat Lank
The paper proves that for a regular Noetherian algebraic stack with quasi-finite diagonal, the derived category of complexes with quasi-coherent cohomology is generated by a single…
Proxy smallness meets -structures
Michal Hrbek, Pat Lank, Giovanna Le Gros +1
The paper defines proxy smallness for t‑structures on triangulated categories over a Noetherian scheme, using tensor actions, and uses this to characterize locally complete interse…
Perfectly generated -structures for algebraic spaces
Michal Hrbek, Pat Lank, Simone Pizzirani
The paper investigates t-structures on the derived category of quasi-coherent sheaves over certain algebraic stacks, proving that the standard t-structure is compactly generated an…
Fppf descent and localizing subcategories for algebraic spaces
Pat Lank
We prove descendability for fppf covers of quasi-compact quasi-separated algebraic spaces. Consequently, we show that point-generatedness is detectable along fppf covers. Moreover,…
A short note on Du Bois singularities
Pat Lank
We study the behavior of Du~Bois singularities under base change and fiber products. For embeddable varieties in characteristic zero, we show that Du~Bois singularities descend fro…