12 papers
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…
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…
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…
Admissible subcategories and metric techniques
Kabeer Manali Rahul
In this work, we provide a way of constructing new semiorthogonal decompositions using metric techniques (à la Neeman). Given a semiorthogonal decomposition on a category with a sp…
Representability theorems via metric techniques
Kabeer Manali Rahul
We prove new Brown representability theorems for triangulated categories using metric techniques as introduced in the work of Neeman. In the setting of algebraic geometry, this giv…
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…
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…
Bounded -structures, finitistic dimensions, and singularity categories of triangulated categories
Rudradip Biswas, Hongxing Chen, Kabeer Manali Rahul +2
Recently, Amnon Neeman settled a bold conjecture by Antieau, Gepner, and Heller regarding the relationship between the regularity of finite-dimensional noetherian schemes and the e…