Relations conjecture for the affine-flag Springer fiber

Let $\textup{Sp}_{q/p}$ be the affine-flag Springer fiber, and let $\epsilon,\xi_1,\ldots,\xi_p,e_2,\ldots,e_p$ be the equivariant classes and parameters defined in the source. Let $I^{(i)}_{q/p}$ be the ideals defined as kernels for the corresponding affine Grassmannian fibers, and let $\pi_i^*$ denote the maps to $\textup{H}^{*}_{\mathbb{G}_m}(\textup{Sp}_{q/p})$. Relations conjecture. The kernel of the surjection

$$\mathbb{Q}[\epsilon,\xi_1,\ldots,\xi_p,e_2,\ldots,e_p]\twoheadrightarrow \textup{H}^{*}_{\mathbb{G}_m}(\textup{Sp}_{q/p})$$

from the generation theorem is generated by $\pi_i^*(I^{(i)}_{q/p})$ for $i=1,\ldots,p$. This conjecturally gives the defining relations for the equivariant cohomology ring; the source says only that a weak version is proved.