8 problems

Corwin–Dan-Cohen's conjecture. For $d\gg 0$,

Let $S$ be a finite set of primes, let $X=\mathbb P^1\smallsetminus\{0,1,\infty\}$, and let $p\notin S$ be a prime. A refinement condition is a tuple…

Let $S$ be a finite set of primes, let $X=\mathbb P^1\smallsetminus\{0,1,\infty\}$, and let $p\notin S$ be a prime. For each depth $n\geq 1$, write $X(\mathbb Z_p)_{S,n}^{\min}$ fo…

Nonvanishing conjecture for the relevant p-adic L-functions. The $p$-adic $L$-function attached to the $\pi$-power-torsion does not vanish at negative powers of $\chi$, and the one…

Global vanishing conjecture.

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…

The symmetrized polylogarithmic Kim conjecture. One has

Let $Z$ be an integer scheme and let $p$ be a prime below $Z$, with $Z$ totally split over $p$. For each $n\in\mathbb{N}$, let … be the associated big polylogarithmic Chabauty–Kim…