The conjecture on equality of F-pure and log canonical thresholds for ideals

Let $\mathfrak{a}$ be an ideal in $\mathbb{Q}[x_1,\ldots,x_m]$, and let $\mathfrak{a}_p=\mathfrak{a}\cdot\mathbb{F}_p[x_1,\ldots,x_m]_{(x_1,\ldots,x_m)}$ be its reduction modulo a prime $p$. Write $\operatorname{fpt}(\mathfrak{a}_p)$ for the $F$-pure threshold of $\mathfrak{a}_p$ at the origin and $\operatorname{lct}(\mathfrak{a})$ for the log canonical threshold of $\mathfrak{a}$ at the origin.

Threshold-equality conjecture. There are infinitely many primes $p$ for which

$$\operatorname{fpt}(\mathfrak{a}_p)=\operatorname{lct}(\mathfrak{a}).$$

For sufficiently large $p$, one has $\operatorname{fpt}(\mathfrak{a}_p)\leq\operatorname{lct}(\mathfrak{a})$ and the $F$-pure thresholds converge to the log canonical threshold. The conjecture asks whether equality holds for infinitely many primes; it remains an open challenge, although cases are known.