4 papers
Derived categories of quadric bundles and moduli stacks of spinor sheaves
Raymond Cheng, Noah Olander
We prove that the Kuznetsov component of a flat family of even-dimensional quadrics of corank at most 2 is equivalent to the twisted derived category of an algebraic space whenever…
A derived category analogue of the Nakai--Moishezon criterion
Daigo Ito, Noah Olander
We give a complete characterization of the line bundles on a proper variety whose tensor powers generate the derived category, answering a 2010 question of Chris Brav. The conditio…
Gerbes for trigonalizable group schemes
Noah Olander, Martin Olsson
We prove that smooth, separated Deligne--Mumford stacks in mixed characteristic with quasi-projective coarse moduli space are global quotient stacks and satisfy the resolution prop…
Approximation by perfect complexes detects Rouquier dimension
Pat Lank, Noah Olander
This work explores bounds on the Rouquier dimension in the bounded derived category of coherent sheaves on Noetherian schemes. By utilizing approximations, we exhibit that Rouquier…