Pareschi–Popa syzygy conjecture for ample line bundles on abelian varieties

Let $X$ be an abelian variety, let $A$ be an ample line bundle on $X$, and let $m(A)$ denote its index of $M$-regularity. For non-negative integers $p\ge m$, Pareschi–Popa's syzygy conjecture. If $m(A)\ge m$, then $A^{\otimes k}$ satisfies property $N_p$ for every $k\ge p+3-m$. This refines the known bounds for syzygies of powers of ample line bundles on abelian varieties by incorporating $M$-regularity; its resolution status is not specified in the source.