9 problems

Let $F$ be an infinite field, let $\overline{\mathcal{L}^{\mathrm{f}}}(F)=\mathcal{L}^{\mathrm{f}}(F)/\mathcal{L}^{\mathrm{f}}_1(F)$, and let $\overline{\delta}^{[k]}$ be the $k$-f…

Let $F_{\varepsilon}=F[\varepsilon]/(\varepsilon^2)$, let ${\cal Q}_{\bullet}(F_{\varepsilon})$ be the scissor-congruence Lie coalgebra, and let…

Goncharov's isomorphism conjecture. The map $\nu_{\bullet,\bullet}^{\cal M}(\mu_N)$ is an isomorphism for either $N=1$, or $N=p$ is a prime and $w=m$.

Let ${\cal C}(G)$ be the refined dihedral Lie coalgebra for a finite commutative group $G$, let ${C}_{\bullet}(G)$ be its graded dual, and let ${\rm Gr}^W{\cal G}^{(l)}$ be the wei…

Let $F$ be a field and consider the cofibre sequence of Lie coalgebras … Let $B_n(F)$ denote the cogenerators in weight $n$. Cofreeness conjecture. The quotient Lie coalgebra…

Let $F$ be a field. The Goncharov Lie coalgebra is … where $\mathscr{G}_n(F)=H_{n,2n-1}^{E_{\infty}}({\mathbf{BGL}}(F)_{\mathds{Q}})$, and its weight-$n$ Chevalley–Eilenberg homolo…

Let $\mathcal{L}(\mathrm{F})$ be the Lie coalgebra filtered by depth, and let $\mathrm{gr}^{\mathcal{D}}_k\mathcal{L}_{2k}(\mathrm{F})$ be its depth-$k$, weight-$2k$ component. Wri…

Let $\mathbb L(F)$ be the Lie coalgebra of multiple polylogarithms over a field $F$, with cobracket $\delta$, and let $\mathbb L^{\operatorname{symb}}(\mathbb C)$ be its symbolic v…

Let ${\cal D}_{\bullet,\bullet}(N)$ be the bigraded dihedral Lie coalgebra associated with $N$-th roots of unity, and let ${\cal C}_{\bullet,\bullet}(N)$ be the depth-graded cyclot…