7 problems

Converse conjecture. If $X$ is Kollár-hyperbolic with respect to $H$, then $X$ is V-hyperbolic with respect to $H$.

Let $k$ be a field with absolute Galois group $G_k$, let $U_1,U_2$ be the curves under consideration, and let $m,n$ be non-negative integers. For each $r$, write…

Let $k$ be a field of characteristic $p\geq 0$, finitely generated over the prime field, with absolute Galois group $G_k$. Let $U$ be an anabelian variety over $k$ with a geometric…

Grothendieck's conjecture. The variety $U$ may be reconstructed group-theoretically from $\pi^{\acute{e}\mathrm{t}}_1(U,\ast)$ and this projection. The conjecture for hyperbolic cu…

Grothendieck's conjecture. The following statements hold:

Finite-determinant conjecture. There exist elements $u\in\mathbb{Z}_{q'}^*$ such that $(\det V,\det\nabla,u\det\Phi)$ corresponds to a finite character of

Let $k$ be a number field, let $X$ be a smooth projective curve over $k$ of genus at least $2$, and fix a geometric point $\bar x$ of $X$. Consider the natural exact sequence … A c…