4 citations · 10 across the 29 of their papers we have counts for
32 papers
Gluing weak approximability along recollements
Pat Lank
We study whether weak approximability glues along recollements of triangulated categories that are compactly generated by a single object. This is applied to derived categories of…
A blowup criterion for regularity
Pat Lank
We prove that a Noetherian integral domain is regular if, and only if, the derived pushforward of the structure sheaf along every blowup is a perfect complex. For suitable local ri…
Fourier--Mukai loci are open and base change
Elías Guisado Villalgordo, Pat Lank
We develop a theory of relative (quasi-)perfect complexes for algebraic spaces. Our main result proves that for a pseudocoherent kernel relatively perfect over both factors, the lo…
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,…
Proxy smallness meets -structures
Michal Hrbek, Pat Lank, Giovanna Le Gros +1
We introduce a notion of proxy smallness for -structures on triangulated categories associated to a Noetherian scheme. Specifically, the theory is developed in the presence of t…
Remarks on diagonal dimension for algebraic stacks
Pat Lank, Fei Peng
This note is concerned with the Rouquier dimension of the bounded derived category of coherent complexes on a Noetherian algebraic stack. Specifically, we study the diagonal dimens…
Dualizing complexes and -structures for algebraic spaces
Pat Lank
This work is concerned with -structures on Noetherian algebraic spaces admitting dualizing complexes. In particular, we study their behavior in the étale topology. As a conseque…
Perfect generation for regular algebraic stacks
Pat Lank
We show that the derived category of complexes with quasi-coherent cohomology on a regular Noetherian algebraic stack with quasi-finite diagonal is generated by a single perfect co…
Fiberwise criteria for Fourier--Mukai equivalences
Elías Guisado Villalgordo, Pat Lank, Kabeer Manali Rahul +1
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…
Frobenius generation for algebraic stacks
Pat Lank, Fei Peng
We introduce a notion of -finiteness for algebraic stacks in positive characteristic. Our main result shows that sufficiently many Frobenius pushforwards generate the bounded de…
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.
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…
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…
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…
Perfectly generated -structures for algebraic spaces
Michal Hrbek, Pat Lank, Simone Pizzirani
This work studies -structures for the derived category of complexes with quasi-coherent cohomology on algebraic spaces. The main result shows that the relative standard -stru…
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…
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…
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…
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…
Measuring rationality of Schwede--Takagi pairs
Pat Lank, Peter McDonald, Sridhar Venkatesh
We begin by giving a derived characterization of rational singularities for pairs in the sense of Schwede--Takagi. This characterization extends a characterization of rational sing…
Descent and generation for noncommutative coherent algebras over schemes
Timothy De Deyn, Pat Lank, Kabeer Manali Rahul
Our work shows forms of descent, in the fppf, h and étale topologies, for strong generation of the bounded derived category of a noncommutative coherent algebra over a scheme. Even…
Approximability and Rouquier dimension for noncommutative algebras over schemes
Timothy De Deyn, Pat Lank, Kabeer Manali Rahul
This work is concerned with approximability (à la Neeman) and Rouquier dimension for triangulated categories associated to noncommutative algebras over schemes. Amongst other thing…
Triangulated characterizations of singularities
Pat Lank, Sridhar Venkatesh
This work presents a range of triangulated characterizations for important classes of singularities such as derived splinters, rational singularities, and Du Bois singularities. An…