4 citations · 10 across the 29 of their papers we have counts for
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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…