11 papers
Categorical characterizations of regularity for algebraic stacks
Timothy De Deyn, Pat Lank, Kabeer Manali Rahul +1
For a Noetherian scheme of finite Krull dimension, Neeman recently established two characterizations of the regularity of using strong generators and bounded -structures…
Coherent sheaves in logarithmic geometry
Hannah Dell, Xianyu Hu, Patrick Kennedy-Hunt +2
This paper introduces an abelian category of logarithmic coherent sheaves that arranges coherent sheaves across all expansions and root stacks of a simple normal crossing degenerat…
Measuring birational derived splinters
Timothy De Deyn, Pat Lank, Kabeer Manali-Rahul +1
This work is concerned with categorical methods for studying singularities. Our focus is on birational derived splinters, which is a notion that extends the definition of rational…
Fiberwise criteria for Fourier--Mukai equivalences
ElÃas Guisado Villalgordo, Elías Guisado Villalgordo, Pat Lank +2
We study the behavior of integral transforms under base change. In particular, we establish a yoga of local algebra and fibers to test for derived equivalences or fully faithfulnes…
A note on quasi-perfect morphisms
Timothy De Deyn, Pat Lank, Kabeer Manali Rahul
This note is concerned with quasi-perfect morphisms between Noetherian algebraic spaces. In particular, we study the local behavior of quasi-perfect proper morphisms. We show that…
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…