This paper studies the derived category of the Quot scheme of rank $ d $ locally free
quotients of a sheaf $\mathscr {G} $ of homological dimension $\le 1$ over a scheme $ X …

In this paper, we study the counterpart of Grothendieck's projectivization construction in the
context of derived algebraic geometry. Our main results are as follows: First, we define the …

This paper establishes semiorthogonal decompositions for derived Grassmannians of
perfect complexes with Tor-amplitude in $[0, 1] $. This result verifies the author's Quot …

Let S be a smooth projective surface over $\mathbb {C} $. We prove that, under certain
technical assumptions, the degeneracy locus of the universal sheaf over the moduli space of …

We define a derived enhancement of the hyperquot scheme (also known as nested Quot
scheme), which classically parametrises flags of quotients of a perfect coherent sheaf on a …

We study torus-equivariant algebraic $ K $-theory of affine Schubert varieties in the perfect
affine Grassmannians over $\mathbb {F} _p $. We further compare it to the torus-equivariant …

Abstract We show that Brill–Noether loci in Hilbert scheme of points on a smooth connected
surface are non-empty whenever their expected dimension is positive and that they are …

For different cohomology theories (including the Hochschild homology, Hodge cohomology,
Chow groups, and Grothendieck groups of coherent sheaves), we identify the cohomology …

We prove a formula for the Chow groups of Quot schemes that resolve degeneracy loci of a
map between vector bundles, under expected dimension conditions. This formula …