The equivariant cohomological Hikita conjecture

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Proves the equivariant cohomological Hikita correspondence for every finite quiver, including loops and multiple arrows, with arbitrary dimension and framing vectors and commuting flavor torus. When every semistable point is stable and the gauge action is free, the equivariant cohomology of the Nakajima variety is canonically the coordinate ring of the scheme-theoretic cocharacter-fixed locus of its flavor-deformed Coulomb branch.

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Theorem 1.1

In The equivariant cohomological Hikita conjecture for arbitrary quivers, 24 September 2026

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For every datum (1.1), every commuting flavor torus F, and every regular stability character \nu, both coefficient maps are surjective and have the same kernel. They therefore induce a canonical isomorphism of graded R-algebras

H_F^*(X;\C)\ \cong\ \C[Y_{\mathfrak f}^{\nu}].

The gradings are ordinary cohomological degree and BFN homological degree, respectively. The assertion includes the empty case, whose ring is zero.

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The equivariant cohomological Hikita conjecture for arbitrary quivers

24 September 2026, current edition.

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We prove the equivariant cohomological Hikita conjecture for arbitrary finite quivers, including loops and multiple arrows. For any dimension and framing vectors, any commuting flavor torus, and a stability character whose semistable locus is stable and has free gauge action, the equivariant cohomology of the Nakajima variety is canonically isomorphic to the coordinate ring of the scheme-theoretic fixed locus of the stability cocharacter on the flavor-deformed Coulomb branch. This is an isomorphism of graded algebras over the common coefficient ring, retaining nilpotents and including the empty case.

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