5 problems

Let $\mathbb{L}$ be the $\overline{\mathbb{Q}}$-linear subspace of $\overline{\mathbb{Q}}_p$ generated by $1$ and the $p$-adic logarithms of nonzero algebraic numbers. Let $N$ be a…

Let $\alpha_1,\ldots,\alpha_n$ be nonzero algebraic numbers. Weak $p$-adic Schanuel conjecture. If $\log_p(\alpha_1),\ldots,\log_p(\alpha_n)$ are linearly independent over…

$p$-adic Structural Rank Conjecture. For every

Let $\widetilde{\mathcal L}\subset\overline{\mathbf Q}_p$ be the $\overline{\mathbf Q}$-vector space generated by $1$ and the elements of $\log_p(\overline{\mathbf Q}^{\times})$. L…

$\ell$-adic Schanuel conjecture. The numbers $\log x_1,\ldots,\log x_n$ are algebraically independent over $\mathbb Q$.