Sheaves on derived spaces

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

Main papers

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.

Six operations

Part (chapter 2) of my thesis, improved + added material. Expected release date: by March 21st. See here for now.

Topological invariance. Joint with Elmanto.

Motivic homotopy theory

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.

K-theory

Thomason’s excess intersection formula for derived stacks.

Projective bundle and blow-up formulas.

A categorification of Milnor excision, with applications to algebraic K-theory of stacks. Joint with Bachmann, Ravi, and Sosnilo.

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

Microlocal theory

Some notes on the Fourier–Sato transform: