Geometry/topology Seminar
Monday, October 18, 2021, 3:15pm, Virtual
Charanya Ravi (University of Regensburg, Mathematics)
Motivic cohomology of algebraic stacks
Abstract:
Algebraic stacks were introduced to study moduli problems in algebraic geometry. These are more general spaces than varieties and one way to understand them is via their cohomological invariants. In this talk, we give a systematic approach to studying the existing cohomology theories for stacks, along with introducing some new cohomology theories. This is achieved by constructing a motivic homotopy theory for stacks. 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 notes: Meeting ID 922 0028 8866

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