Here are some papers and notes about sheaves on derived spaces/stacks and their cohomology and Borel–Moore homology.

Contains most of the derived geometry prerequisites for the below papers. (Joint with Rydh.)

The main paper constructing Borel–Moore homology, cohomology, and fundamental classes of derived stacks. Preliminary draft (revision expected by March 21st).

The formalism that the above paper builds on. Joint with Déglise and Jin.

A K-theoretic counterpart to the cohomology and Borel–Moore homology stuff above.

An improved version of chapter 2 of my thesis. Preliminary draft, some more material to be added later (expected release date: by March 21st).

Topological invariance. Joint with Elmanto.

Papers dealing specifically with the stable motivic homotopy category.

Discusses the role of virtual classes in motivic homotopy theory. Joint with Elmanto, Hoyois, Sosnilo, and Yakerson.

Subsumes part (chapter 1) of my thesis.

Thomason’s excess intersection formula for derived stacks.

Projective bundle and blow-up formulas.

Excision for Milnor and blow-up squares. Joint with Bachmann, Ravi, and Sosnilo.

Homotopy invariant K-theory and the Bass construction over the sphere spectrum. Joint with Cisinski.

Some notes on the Fourier–Sato transform:

1. Overview (2020-01-08)

2. Constructible categories and localization (2020-01-15)

3. The Euler transformation (2020-01-26)

4. A **G**_{m}-equivariant sheaf on the affine line (2020-02-01)

5. The homotopy lemma (2020-02-09)

6. Total spaces of perfect complexes (2020-02-12)

7. Homotopy invariance for perfect complexes (2020-02-12)

8. The Fourier–Sato transform (2020-02-16)

9. Involutivity (2020-02-16)

10. The square of ^{^}j_*(1) (2020-02-17)

11. Involutivity: reduction (2020-03-01)

12. Involutivity: connective case (2020-03-01)

13. A functoriality property (2020-03-02)

14. Involutivity: coconnective case (2020-03-13)