# Generalized cohomology theories for algebraic stacks

@inproceedings{Khan2021GeneralizedCT, title={Generalized cohomology theories for algebraic stacks}, author={A. Khan and Charanya Ravi}, year={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 category represent generalized cohomology theories for stacks like algebraic K-theory, as well as new examples like genuine motivic cohomology and algebraic cobordism. These cohomology theories admit Gysin maps and satisfy homotopy invariance, localization, and Mayer–Vietoris. We also prove a fixed point… Expand

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