5 problems

Let $X$ be a regular projective curve over an algebraically closed field $k$, and let $F=k(X)^*$. Let ${\cal B}_2(k)$ and ${\cal B}_3(F)$ be the Bloch groups with boundary maps…

Refined Colmez conjecture. There exists an integer $m\geq1$ and an element $\beta=\beta(A,m,\phi)\in\omega_{\cal A}^{\otimes m}$ such that (a) $\beta$ generates…

Goncharov's strong Suslin reciprocity conjecture. The map $\mathcal H_{k(X)}$ should satisfy both

Let $F$, $C_{\mathfrak f}$, $D$, $\mathfrak a_c$, $\pi_{\mathfrak q}$ and $\mathfrak p$ be as in the preceding subsection. Let $\Phi_\tau$ be the $\tau$-semilinear action on…

Assume that $\dim X=1$. Let $P$ be the weight group of $\Delta_{\hat\Pi}$, let $Q\subset P$ be the subgroup generated by the roots, and let…