We develop a theory of unbounded derived categories of quasi-coherent sheaves on
algebraic stacks. In particular, we show that these categories are compactly generated by …

We formulate a version of the integral Hodge conjecture for categories, prove the conjecture
for two-dimensional Calabi–Yau categories which are suitably deformation equivalent to the …

We develop a version of Hodge theory for a large class of smooth formally proper quotient
stacks X∕ G analogous to Hodge theory for smooth projective schemes. We show that the …

We compute the Hochschild cohomology of Hilbert schemes of points on surfaces and
observe that it is, in general, not determined solely by the Hochschild cohomology of the …

K-2mu-theory and the singularity category of quotient singularities Page 1 ANNALS OF K-THEORY
A JOURNAL OF THE K-THEORY FOUNDATION msp vol. 6 no. 3 2021 K-theory and the …

Motivated by the local flavor of several well-known semi-orthogonal decompositions in
algebraic geometry, we introduce a technique called conservative descent, which shows …

We study the Hodge theory of twisted derived categories and its relation to the period-index
problem. Our main contribution is the development of a theory of twisted Mukai structures for …

Let X be a smooth and tame stack with finite inertia. We prove that there is a functorial
sequence of blow-ups with smooth centers after which the stabilizers of X become abelian …

We prove smoothness in the dg sense of the bounded derived category of finitely generated
modules over any finite-dimensional algebra over a perfect field, hereby answering a …

We prove Kontsevich's homological mirror symmetry conjecture for certain mirror pairs
arising from Batyrev–Borisov's 'dual reflexive Gorenstein cones' construction. In particular …