68 problems

Let $X$ be a smooth variety over a field of characteristic zero, and let $H^3(\Gamma(X,4))$ denote the third cohomology of Goncharov's weight-four polylogarithmic complex on $X$. L…

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…

Pour $n\geq 1$, soit $\iota^\bullet(n):\mathcal{B}^\bullet(F,n)\rightarrow\mathrm{CE}^\bullet(\mathcal{C}(F))_n$ le morphisme de complexes induced by motivic polylogarithms. Conjec…

Soient $F$ un corps de nombres et $n\geq 2$. Notons $d_n=r_1+r_2$ si $n$ est impair et $d_n=r_2$ si $n$ est pair, et soit…

For a positive integer $p$, let $B_r$ denote the Bernoulli numbers, let $H_n=\sum_{k=1}^n 1/k$ be the harmonic numbers, and let $H_n^{(2)}=\sum_{k=1}^n 1/k^2$ be the second-order h…

The paper considers the coefficients in the left-hand side of formula (12), expressed using the quantities $G_0(k,n,s;1)$. Coefficient and Ohno–Zagier conjecture. All coefficients…

Let $T\mathcal M(n)$ denote the additive part of the degree-$n$ component of the indecomposable space, and let $Z_n(a)$ be a codimension-$n$ cycle on … For $a\in\mathbb A^1-\{0\}$,…

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…

Let $\widehat G_{n-1}^n$ be the configuration space used to define the Grassmannian $n$-logarithm, and let $a_i,b_j$ be the maps on this space appearing in its functional equations…

Let $F$ be a field. Let $B_2(F)$ be the Bloch group, let $R_3(F)$ be the subgroup generated by the stated relations in ${\mathbb Z}[{\mathbb P}^1_F]$, and define … Let…

Let $G_4(F)$ be the weight-four Grassmannian group, let $\mathcal B_4(F)$ be the corresponding polylogarithmic group, and let … be the canonical cobracket described in the construc…

Weight-four inverse map conjecture. There exists a map

Let $\widetilde A_n$ be the free abelian group generated by admissible pairs of simplices, let $\overline C_{2n}$ be the Grassmannian configuration group, and suppose the maps…

Let $F$ be a field, and let $\overline C_{2n}(F)$ denote the configuration group used for Grassmannian $n$-logarithms. Let $R_i(n)$ be varieties over $\mathbb Z$, and let … be morp…

Goncharov's quasi-isomorphism conjecture. The complex $\Gamma(F;n)$ should be quasi-isomorphic to the weight $n$ motivic complex of $\operatorname{Spec}(F)$; equivalently,

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, let $B_n(F)$ be Goncharov's polylogarithmic group, and let … be the associated map. Write $K^{(n)}_{2n-1}(F)_\mathbb Q$ for the $n$-th graded quotient of the…

Let $R_1^*$ denote the Flint Hills series and let $tau=frac{1-frac{1}{2} u}{?}$ be... There exist rational constants $c1,c2 obreaktext{ in } obreakbb Q$ such that … By Theorem, thi…

Let $k$ be as in the preceding theorem, let $calpha,cbeta$ be the parameters in the narrow ideal-class partial zeta value $czeta(k,(calpha,cbeta),cscrB)$, and let $cscrB^*$ denote…

Let $C$ be a cone, and let $A_C$ be the matrix associated with its generating vectors. Let $N$ denote the integer appearing in the description of the corresponding conical zeta val…

Let $V(z)$ denote the polylogarithmic variation of mixed Hodge structure over $\mathbb{P}^1\backslash\{0,1,\infty\}$, with its fibers and extension data described by the polylogari…

Let $F$ be an infinite field. Let $B_3(F)$ be Goncharov's Bloch group defined using the stated relations, and let $\mathcal{L}^{\mathrm{f}}_3(F)$ be the weight-three component of t…

Let $F$ be an infinite field, let $1\leq i\leq n$, and let $\mathcal{H}^{\mathrm{f}}(F)$ denote the formal Hopf algebra with weight-$n$ cohomology…

Let $F$ be a subfield of $\mathbb{C}$, and let $\mathcal{H}^{\mathrm{f}}_n(F)$ be the weight-$n$ part of the formal Hopf algebra constructed in the paper. Let … be the motivic real…

Let $K$ be an imaginary quadratic field, let its partial zeta function mean the zeta function attached to a specified ideal class (equivalently, a partial zeta function of $K$), an…