Hindry–Ratazzi's torsion-growth conjecture for abelian varieties

Let $A$ be an abelian variety isogenous to a product

$$\prod_{i=1}^d A_i^{n_i},$$

where the $A_i$ are simple abelian varieties that are pairwise non-isogenous. Let $\gamma(A)$ be the optimal exponent governing the growth of $|A(L)_{\mathrm{tors}}|$ as $L/K$ ranges over finite extensions, and let $\operatorname{MT}(A)$ denote the Mumford–Tate group of $A$. Hindry–Ratazzi's conjecture. One has

$$\gamma(A)=\max_{\emptyset\neq I\subset\{1,\ldots,d\}}\frac{2\sum_{i\in I}n_i\dim A_i}{\dim\operatorname{MT}(A)}.$$

This conjecture proposes an optimal formula for the polynomial growth exponent of torsion over finite extensions of a number field, extending explicit formulas known in several cases, including products of elliptic curves, CM-type abelian varieties, and suitable varieties of symplectic-similitude type. Its general validity is not established in the supplied text.