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Friday, October 22, 2021

**Abstract:** Equivariant motivic homotopy theory is the homotopy theory of motivic spaces and spectra with algebraic group actions. Following [Hoy17], I will introduce both the unstable and stable equivariant motivic homotopy ∞-category. I will also talk about the so called Ambidexterity Theorem which identifies the left and right adjoint of the pullback functor f* up to a suspension. Then I will show how to prove the Atiyah Duality by using the Ambidexterity and some other properties of these functors. [Hoy17] Marc Hoyois, The six operations in equivariant motivic homotopy theory.