19 problems

Let $X$ be a smooth projective variety defined over $\overline{\mathbb{Q}}$, and let $\mathrm{H}^{n}_{\mathrm{dRB}}(X,\mathbb{Q})$ be its de Rham–Betti structure. Write…

Let $X$ be a smooth projective variety defined over $\overline{\mathbb{Q}}$, and let $0\leq j\leq\dim(X)$ be an integer. Consider the de Rham-Betti structure … If…

Grothendieck's de Rham-Betti cycle conjecture. Every de Rham-Betti class in $V_{\mathrm{B}}$ comes from a $\mathbb{Q}$-coefficient algebraic cycle on $X$ for $0\leq p\leq \dim(X)$.…

Let $A$ and $B$ be the varieties appearing above, and consider the mixed motive $H^1(A,A\cap B)$ together with its exact sequence … Here $\mathbb{Q}(0)$ denotes the Tate motive of…

André's generalized Grothendieck period conjecture. One has

Let $K$ be a number field with algebraic closure $\bar K$ in $\mathbb{C}$, let $X$ be a smooth projective $K$-variety, and let $H^*_{dR}(X)$ and $H^*_B(X)$ be its de Rham and Betti…

Let $M$ be a motive, let $\langle M\rangle$ be the category it generates, and let $p$ be a prime. Let $H(M)$ be the relevant homogeneous space, let $\operatorname{eval}$ be the eva…

Weak abelian Schanuel conjecture.

Let $\operatorname{red}_{\zeta}$ be the map obtained by reducing $p$-adic multiple zeta values modulo sufficiently large primes, from the $\mathbb{Q}$-algebra of $p$-adic multiple…

Fix $N>1$ and work on $\mathbb{P}^{1}-\{0,\mu_N,\infty\}$. Let $p$ range over primes not dividing $N$, let $\alpha\in\mathbb{N}$, and let $\operatorname{har}_{p^{\alpha}}$ denote t…

Let $\mathcal{P}_{\geq 3}$ denote the set of primes at least $3$, let $\alpha\in\mathbb{N}^{\ast}$, and let $I$ be one of $\mathcal{P}_{\geq 3}\times\{\alpha\}$,…

Let multiple zeta values be the numbers obtained from convergent multiple zeta series, and consider the double-shuffle, associator and Kashiwara–Vergne relations among them. Relati…

Let $Z$ be an integer scheme with fraction field $K$, and let $\mathfrak{p}$ be a closed point of $Z$. Let … be the $p$-adic period map associated with Besser–Coleman integration.…

Let $C$ be the base curve, let ${\mathcal A}$ be the abelian scheme appearing in the source, and let … The two groups are compared after tensoring with $\mathbb C$ via the de Rham–…

Let $X$ be a smooth projective variety over ${\overline{\mathbb Q}}$. A pair $(\alpha,\beta)$ belongs to…

Standard-level sharpness conjecture. If $N$ is a standard level, the standard relations always give the sharp bound for $d(w,N)$; equivalently, all linear relations derive from the…

Non-standard-relation conjecture. Non-standard relations do not exist; equivalently, $SR(N)$ is sharp. The source reports verification only for the first two prime squares, $N=25$…

Binary-index conjecture. If $N=3$ or $N=4$, every MPV of level $N$ is a linear combination of MPVs

Level-three MPV conjecture. When $N=3$, all linear relations among MPVs are consequences of the RDS and lifted RDS, and