13 problems

Let $D_2$ be the Bloch–Wigner dilogarithm, and consider its values $D_2(z)$ at algebraic arguments $z$. Zagier's conjecture. Every rational linear relation among these values is a…

Let $\mathcal B(\mathbb C)$ be the Bloch group, defined as the kernel of the complex Dehn invariant, and let … be the Bloch regulator map. Bloch regulator injectivity conjecture. T…

Let $E=\overline{E}\subset\mathbb{C}$ be a conjugation-stable field, let $\mathcal B(E)$ be its Bloch group, and let $\rho:\mathcal B(E)\to\mathbb{C}/\mathbb{Q}(2)$ be the Bloch re…

For an integer $N\geq 3$, let $D_2$ denote the Bloch–Wigner dilogarithm, and consider the real numbers $D_2(e^{2\pi\sqrt{-1}j/N})$ indexed by integers $j$ relatively prime to $N$ w…

Optimistic-limit volume conjecture. There exists a solution $(x_0,y_0)$ to

Uniqueness and maximality conjecture. This is the only eighth-degree, two-term dilogarithm combination that admits a closed form, and it is the highest-degree identity of this form…

Let $\mathcal{C}^{\underline{a}}_{m,n}$ be the family of curves cut out by $F^{\underline{a}}_{m,n}$, and let $R_{\gamma_1}(\underline{a})$ be the regulator period asymptotic to…

Rigidity conjecture. For every field $F$, this natural map is an isomorphism. The conjecture would imply the isomorphism used in the paper for function fields and would support des…

Let $D\colon \mathbb{C}\setminus\{0,1\}\to\mathbb{R}$ be the Bloch–Wigner dilogarithm. A functional equation of $D$ is an identity obtained from values of $D$ at expressions in its…

Let $\operatorname{Li_2}(z)$ be the dilogarithm, let $w_0$ be the unique solution of … with $w_0\approx 0.916198+0.182459i$, and define … Thus $w_0=1-e^{-2\pi i z_0}$ and…

Let $E$ be an elliptic curve over a number field $F$, and let $d=[F:\mathbf{Q}]$. Let $\mathcal{A}_{E/F}\subset \mathbf{Z}[E(\overline{\mathbf{Q}})]^{G_F}$ be the subgroup of divis…

Dilogarithm conjecture. For this real positive solution, the dilogarithm identity stated immediately after the candidate holds.

Let $A$ be a positive definite symmetric $r\times r$ matrix with rational coefficients. Let $(Q_1,\dots,Q_r)$ range over the solutions in number fields of the algebraic system … ma…