Deligne's rationality conjecture for critical motives

Let $M$ be a critical motive over $K$ with coefficient field $\mathcal{F}$. Let $\gamma$ and $\delta$ be $\mathcal{F}$-bases of ${\det}_\mathcal{F}(H_B(M)^+)$ and ${\det}_\mathcal{F}(t(M))$, respectively, and let $\Omega_{\gamma,\delta}$ be defined by the determinant of the period map. Deligne's conjecture. One has

$$\frac{L(M,0)}{\Omega_{\gamma,\delta}}\in\mathcal{F}.$$

This is the rationality part of the Tamagawa number conjecture and is known in important cases; the source presents it as a conjecture without asserting a general resolution.