A complete and chronologically ordered list of my preprints and publications is here.
For beginners to derived algebraic geometry, I recommend starting with stacksncts or blowups.
Virtual fundamental classes, virtual localization, virtual structure sheaves:
| virtual | Virtual fundamental classes of derived stacks I |
| virloc | Virtual localization revisited (with D. Aranha, A. Latyntsev, H. Park, C. Ravi) |
| kstack | K-theory and G-theory of derived algebraic stacks (§ 6) |
Derived microlocalization and Fourier transforms:
| dimredcoha | 3d cohomological Hall algebras for local surfaces (with T. Kinjo) |
| fourier | The derived homogeneous Fourier transform |
| modfour | Modularity of higher theta series II (with T. Feng) |
Equivariant cohomology, concentration and localization:
| equilisse | Equivariant generalized cohomology via stacks (with C. Ravi) |
| constack | The stacky concentration theorem (with D. Aranha, A. Latyntsev, H. Park, C. Ravi) |
| concat | Cohomological and categorical concentration (with C. Ravi) |
Constructions of six functor formalisms:
| six | Voevodsky's criterion for constructible categories of coefficients |
| sixstack | Generalized cohomology theories for algebraic stacks (with C. Ravi) |
| virtual | Virtual fundamental classes of derived stacks I (Appendix A) |
| weavelisse | Lisse extensions of weaves |
Algebraic K-theory of derived schemes and stacks:
| kstack | K-theory and G-theory of derived algebraic stacks |
| kblow | Algebraic K-theory of quasi-smooth blow-ups and cdh descent |
| excess | Virtual excess intersection theory |
| milnor | Categorical Milnor squares and K-theory of algebraic stacks (with T. Bachmann, C. Ravi, V. Sosnilo) |
| lettuce | The lattice property for perfect complexes on singular stacks |
Elliptic cohomology:
| ellhodge | Elliptic loop spaces (with E. Bouaziz) |
Fundamental classes and intersection theory in terms of the six functors:
| fund | Fundamental classes in motivic homotopy theory (with F. Déglise, F. Jin) |
| dualet | Absolute Poincaré duality in étale cohomology |
Abstract six functor formalisms:
| thesis | Motivic homotopy theory in derived algebraic geometry |
| weaves | Weaves |
| weavelisse | Lisse extensions of weaves |
Foundational stuff about derived algebraic geometry:
| blowups | Virtual Cartier divisors and blow-ups (with D. Rydh) |
| classicality | Dimensional classicality criterion for derived stacks |
| deloop | Motivic infinite loop spaces |
| deloop2 | Framed transfers and motivic fundamental classes |
| deloop3 | Modules over algebraic cobordism |
| deloop4 | On the infinite loop spaces of algebraic cobordism and the motivic sphere (EHKSY + Bachmann) |
| thesis | Motivic homotopy theory in derived algebraic geometry |
| localization | The Morel–Voevodsky localization theorem in spectral algebraic geometry |
| a1-sag | A1-homotopy invariance in spectral algebraic geometry (with D.-C. Cisinski) |