K-theory and G-theory of derived algebraic stacks
@article{Khan2022KtheoryAG, title={K-theory and G-theory of derived algebraic stacks}, author={Adeel A. Khan}, journal={Japanese Journal of Mathematics}, year={2022} }
These are some notes on the basic properties of algebraic K-theory and G-theory of derived algebraic spaces and stacks, and the theory of fundamental classes in this setting.
4 Citations
The Log Product Formula in quantum $K$-theory
- Mathematics, Computer Science
- 2020
We prove a formula expressing the $K$-theoretic log Gromov-Witten invariants of a product of log smooth varieties $V \times W$ in terms of the invariants of $V$ and $W$. The proof requires…
Generalized cohomology theories for algebraic stacks
- Mathematics
- 2021
We extend the stable motivic homotopy category of Voevodsky to the class of scalloped algebraic stacks, and show that it admits the formalism of Grothendieck’s six operations. Objects in this…
Foliations and stable maps
- Mathematics
- 2022
This paper is part of an ongoing series of works on the study of foliations on algebraic varieties via derived algebraic geometry. We focus here on the specific case of globally defined vector fields…
Virtual excess intersection theory
- MathematicsAnnals of K-Theory
- 2021
We prove a K-theoretic excess intersection formula for derived Artin stacks. When restricted to classical schemes, it gives a refinement, and new proof, of R. Thomason's formula.
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