A Geometric Proof of Mordell's Conjecture for Function Fields
| dc.creator | Li, Kezheng | |
| dc.date | 2007-01-15 | |
| dc.date.accessioned | 2026-07-07T07:41:01Z | |
| dc.date.available | 2026-07-07T07:41:01Z | |
| dc.description | Let $\Cal C,\Cal C'$ be curves over a base scheme $S$ with $g(\Cal C)\ge 2$. Then the functor $T\mapsto\{$generically smooth $T$-morphisms $T\times_S\Cal C'\to T\times_S\Cal C\}$ from $((S$-schemes)) to ((sets)) is represented by a quasi-finite unramified $S$-scheme. From this one can deduce that for any two integers $g\ge 2$ and $g'$, there is an integer $M(g,g')$ such that for any two curves $C,C'$ over any field $k$ with $g(C)=g$, $g(C')=g'$, there are at most $M(g,g')$ separable $k$-morphisms $C'\to C$. It is conjectured that the arithmetic function $M(g,g')$ is bounded by a linear function of $g'$. | |
| dc.description | 15 pages | |
| dc.identifier | https://arxiv.org/abs/math/0701407 | |
| dc.identifier | http://arxiv.org/abs/math/0701407 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/121958 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 14H05;14H10;14G27 | |
| dc.title | A Geometric Proof of Mordell's Conjecture for Function Fields | |
| dc.type | text |