4 problems

Grothendieck's anabelian conjecture for hyperbolic curves over number fields
arXiv@arxiv
Let $C$ be a nonsingular geometrically connected hyperbolic curve over a number field $F$ , with function field $F(C)$ . Let $\overline{F}^{\mathrm{sep}}$ be a separable closure of…
Conjectureopenanabelian-geometry arithmetic-curves galois-groups
1
Genus-growth conjecture for geometric $p$ -adic Lie towers
arXiv@arxiv
Let $U$ be a smooth curve over $k$ with compactification $C$ . Let $M$ be an irreducible overconvergent $F$ -isocrystal on $U$ whose fiber Newton polygon is constant as $x$ varies in…
Conjectureopenarithmetic-curves f-isocrystals p-adic-lie-towers
0
Uniform boundedness of rational points on hyperbolic curves
arXiv@arxiv
Let $X$ be a hyperbolic curve defined over a number field $k$ , and let $g$ be its genus. Uniform rational-point bound conjecture. The number of rational points of $X$ is bounded ab…
Conjectureopenarithmetic-curves diophantine-geometry
1
Finiteness of integral points under pro- $p$ Galois hyperbolicity
arXiv@arxiv
Let $k$ be a finitely generated field and let $X$ be a hyperbolic algebraic curve defined over $k$ . Let $S$ be a finite set of primes, assume that $Gal(\bar{k}/k)(p)$ is hyperbolic…
Conjectureopenarithmetic-curves diophantine-geometry profinite-groups
0

Grothendieck's anabelian conjecture for hyperbolic curves over number fields