Beilinson–Goncharov–Schechtman–Varchenko's hyperplane-arrangement generation conjecture

Let $k$ be a number field. Given hyperplanes $L_i$ and $M_i$, for $i=0,\ldots,n$, in general position in $\mathbb P^n$ and defined over $k$, consider the mixed Tate motive

$$\mathfrak m(\mathbb P^n\smallsetminus M,L\smallsetminus(L\cap M)).$$

Its realizations give the middle-dimensional relative cohomology

$$H^n(\mathbb P^n\smallsetminus M,L\smallsetminus(L\cap M)).$$

Let $\mathcal C$ be the subcategory of the category $\mathcal{M}\mathcal{T}(k)$ of mixed Tate motives over $k$ generated by these motives. Beilinson–Goncharov–Schechtman–Varchenko conjecture. The subcategory $\mathcal C$ is all of $\mathcal{M}\mathcal{T}(k)$.

The conjecture proposes that motives arising from hyperplane arrangements in general position generate the entire category of mixed Tate motives over a number field; the surrounding text attributes further elaboration of this framework to Nori.