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Motivic cohomology of algebraic stacks

Geometry/topology Seminar
Monday, October 18, 2021
3:15 pm - 4:15 pm
Charanya Ravi
Geometry/topology Seminar

We discuss the constructions of a 'genuine' and a 'limit-extended' motivic homotopy category for algebraic stacks along with the formalism of six operations. Objects in these categories represent generalized cohomology theories for stacks like algebraic K-theory, motivic cohomology, algebraic cobordism, and their quadratic refinements namely hermitian K-theory, Milnor-Witt motivic cohomology, and special linear algebraic cobordism. In the case of quotient stacks, the respective constructions give Bredon-type and Borel-type equivariant cohomology theories. We review these constructions and discuss some properties. This is joint work with Adeel Khan.

Zoom meeting ID: 922 0028 8866
Zoom meeting password: 043757