Fontaine–Perrin-Riou's order-of-vanishing conjecture for motivic L-functions

Let $M$ be an $L$-admissible premotivic structure over $K$, let $\tau:K\to\mathbb{C}$ be an embedding, and let $\lambda$ be any finite prime of $K$. Write $M^D=\operatorname{Hom}_K(M,K(1))$ and let $M^D_\lambda$ be its $\lambda$-adic realization. Fontaine–Perrin-Riou's order-of-vanishing conjecture.

$$\operatorname{ord}_{s=0}L(M,\tau,s)=\dim_{K_\lambda}H^1_f(\mathbb{Q},M^D_\lambda)-\dim_{K_\lambda}H^0(\mathbb{Q},M^D_\lambda).$$

This predicts that the order of vanishing at the central point is governed by the Bloch–Kato finite Selmer group, after subtracting the dimension of the global invariants. It is stated as a general conjecture for $L$-admissible premotivic structures.