For regular G-actions on smooth projective X, the G-equivariant cohomology ring of X is isomorphic to the coordinate ring of a regular fixed point scheme.
In Pa- rameter Spaces, volume 36 of Banach Center Publications , 25–44
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Spectrum of equivariant cohomology as a fixed point scheme
For regular G-actions on smooth projective X, the G-equivariant cohomology ring of X is isomorphic to the coordinate ring of a regular fixed point scheme.