8 problems

Let $\mathfrak{g}^*$ be the homotopy Lie algebra associated with the free massless theory in dimension $d$, and let $G_{M,\mathrm{Betti}}$ be the motivic Galois group in the Betti…

Let $P_{\mathbb{Z},\mathrm{Tate}}$ be the subalgebra of periods generated by $(2\pi i)^{\pm1}$ and periods of mixed Tate motives unramified over $\mathsf{Spec}(\mathbb{Z})$. Let th…

Let $\mathcal{MTM}(\mathbb{Z})$ be the Tannakian category of mixed Tate motives over $\mathbb{Z}$, and let $\mathcal{G}_{1}=\mathbb{G}_{m}\ltimes\mathcal{U}_{1}$ be its motivic Gal…

Let $(X,\tilde X)$ and $(X',\tilde X')$ be pairs as in the paper, with a morphism $(X',\tilde X')\to(X,\tilde X)$, and let…

Let $K_*=(K_n)_n$ be the tower of motivic groups arising from the moduli spaces $\mathcal{M}_{0,n}$, and let $\mathcal{R}_{\mathrm{Betti}}(K_*)$ and…

Let $D\simeq\mathcal{M}_{0,n_1}\times\mathcal{M}_{0,n_2}$ be a codimension-one boundary component, and let $K^{\bullet}_{\mathbb{Z},n_1,n_2}$ denote the geometric derived group ass…

Over $\operatorname{Spec}(\mathbb{Z})$, let $G^{\bullet}_{\mathbb{Z},n}$ be the affine derived group scheme associated with the mixed Tate category of $\mathcal{M}_{0,n}$, and let…

Let $E$ be a motive over $K$, and let $G_{\mathcal{M}(E)}$ denote its motivic Galois group. Serre's domination by maximal motives conjecture. After replacing $K$ by a finite extens…