The de Rham–Betti conjecture

Let $M$ be an André motive over $K$, or a homological motive over $K$. Write $\Omega_M^{\mathrm{dRB}}$ for the torsor of de Rham–Betti periods, $\Omega_M^{\mathrm{And}}$ for the torsor of motivated periods, and $\Omega_M^{\mathrm{mot}}$ for the torsor of motivic periods. The de Rham–Betti conjecture. For an André motive, the inclusion

$$\Omega_M^{\mathrm{dRB}}\subseteq\Omega_M^{\mathrm{And}}$$

is an equality; for a homological motive, the inclusions

$$\Omega_M^{\mathrm{dRB}}\subseteq\Omega_M^{\mathrm{And}}\subseteq\Omega_M^{\mathrm{mot}}$$

are equalities. This is a special instance of Grothendieck's period conjecture; the source does not claim it is known in general.