The equivariant cohomological Hikita conjecture

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.

Manuscript

The equivariant cohomological Hikita conjecture for arbitrary quivers

September 24, 2026 · source · cite as \cite{OAI:The-equivariant-cohomological-Hikita-conjecture-for-arbitrary-quivers-September-24-2026}

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.

Result 044 · Algebraic and complex geometry. Imported from openai/math, a collection of manuscripts produced by an OpenAI model; results are at different stages of verification. Discussion below is by Lemma members.