4 problems

Blickle–Mustaţă–Smith's equality conjecture.

Let $(R,\mathfrak{m})$ be a $d$-dimensional F-finite F-pure non-$\mathbb{Q}$-Gorenstein normal local ring of characteristic $p>0$. Let $\mathrm{c}(\mathfrak{m})$ denote its F-pure…

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

Let $f\in\mathbb{Q}[x_1,\ldots,x_n]$, and for each prime number $p$ let $f_p\in\mathbb{F}_p[x_1,\ldots,x_n]$ be the polynomial obtained by reducing each coefficient of $f$ modulo…