General form of averaged Igusa conjecture for exponential sums

Let $K$ be a number field, let $\mathcal{I}\subset\mathcal{O}_K[x_1,\dots,x_n]$ be a non-zero ideal with $\mathcal{I}_K\neq(1)$, and let $Z\subset\mathbb{A}^n_{\mathcal{O}_K}$ be a subscheme. For each positive integer $r$, let $E_{L,Z,\mathcal{I}}^{(r)}(m)$ be the associated averaged exponential sum and let $\operatorname{moi}_{K,Z}^{(r)}(\mathcal{I})$ be the averaged motivic oscillation index. General averaged Igusa conjecture. There exist an integer $M$, depending only on $\mathcal{I}$, and a positive constant $c_r$, depending only on $\mathcal{I}$ and $r$, such that for all $L\in\widetilde{\mathcal{L}}_{K,M}$ and all $m\geq2$,

$$\left|E_{L,Z,\mathcal{I}}^{(r)}(m)\right|\leq c_r m^{n+r-1}q_L^{-m\operatorname{moi}_{K,Z}^{(r)}(\mathcal{I})}.$$

This conjecture is obtained by specializing the general polynomial conjecture to linear combinations of generators of an ideal. It is not resolved in the source.