Nonexistence of singly compactly generated $t$-structures for schemes
Anirban Bhaduri, Timothy De Deyn, Michal Hrbek, Pat Lank, Kabeer Manali-Rahul
TL;DR
This paper demonstrates that for certain schemes, the standard aisles in their derived categories of quasi-coherent sheaves cannot be generated by a single compact object, revealing limitations in the structure of these categories.
Contribution
It provides the first examples of schemes with standard aisles that are not singly compactly generated in their derived categories.
Findings
Standard aisles on derived categories of some schemes are not singly compactly generated.
First known instances of such schemes with this property.
Highlights limitations in the generation of derived categories for schemes.
Abstract
We show the first instances of schemes whose standard aisles on their derived category of quasi-coherent sheaves are not singly compactly generated.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Algebraic Geometry and Number Theory · Homotopy and Cohomology in Algebraic Topology