The center conjecture for cyclotomic Hecke algebras and cohomology of quiver varieties

For a quiver without edge loops, we construct an isomorphism from the cohomology of a Nakajima quiver variety with coefficients in an arbitrary field to the Jucys--Murphy center of the corresponding cyclotomic KLR algebra over that field. In affine type $A^{(1)}_{e-1}$, combining this with a dimensi