Equivariant generalized cohomology via stacks

Abstract

We prove a general form of the statement that the cohomology of a quotient stack can be computed by the Borel construction. It also applies to the lisse extensions of generalized cohomology theories like motivic cohomology and algebraic cobordism. As a consequence, we deduce the localization property for the equivariant algebraic bordism theory of Deshpande-Krishna-Heller-Malagón-López. We also give a Bernstein-Lunts-type gluing description of the ∞-category of equivariant sheaves on a scheme X, in terms of nonequivariant sheaves on X and sheaves on its Borel construction.

Equivariant Cobordism of Smooth Projective Spherical Varieties

“…Lemma 2. 16 Let T be a torus of rank n and F be a finite subgroup. Then we have a graded L-algebra isomorphism *…”

Discrete-Time Fourier Transform Discrete Fourier Transform

“…A]). In general, D only satisfies Nisnevich descent, so we need to restrict our attention to Nis-Artin stacks (see [Kha2,§4], [KR,§1]). For τ ∈ {Nis, ét} we define (τ, n)-Artin and τ -Artin stacks as in [KR, 0.2.2]:…”