Nonexistence of singly compactly generated $t$-structures for schemes
We show the first instances of schemes whose standard aisles on their derived category of quasi-coherent sheaves are not singly compactly generated.
math.AG↗
arXiv subjects
Kabeer Manali-Rahul
Publications and source records attributed to Kabeer Manali-Rahul.
Measuring birational derived splinters
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 singularities beyond varieties over fields of characteristic zero. Particularly, we show that an invariant called `level' in the associated derived category measures the failure of these singularities.
math.AG↗
Classification and nonexistence for $t$-structures on derived categories of schemes
Given a suitable Noetherian scheme, we classify tensor $t$-structures on the bounded derived category of coherent sheaves and its variants with prescribed support. Furthermore, we show that the existence of such $t$-structures restricting to perfect complexes detects regularity, recovering a theorem of Neeman in the affine case by different methods. Our tools establish local-to-global principles for tensor $t$-structures.
math.AG↗