9 problems

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 $0\leq p\leq \dim(X)$.…

André's generalized Grothendieck period conjecture. One has

The p-adic period conjecture. For every open integer scheme $Z$, the period map $\operatorname{per}_{\pf}\colon A(Z)\to\mathbb{Q}_p$ is injective. This is presented as a $p$-adic a…

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 $\mathcal{P}_{\geq 3}\times\{\alpha\}$,…

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