Hyperelliptic jacobians with real multiplication
| dc.creator | Elkin, Arsen | |
| dc.date | 2004-03-31 | |
| dc.date | 2005-03-04 | |
| dc.date.accessioned | 2026-07-07T05:06:57Z | |
| dc.date.available | 2026-07-07T05:06:57Z | |
| dc.description | Let $K$ be a field of characteristic $p \neq 2$, and let $f(x)$ be a sextic polynomial irreducible over $K$ with no repeated roots, whose Galois group is isomorphic to $\A_5$. If the jacobian $J(C)$ of the hyperelliptic curve $C:y^2=f(x)$ admits real multiplication over the ground field from an order of a real quadratic field $D$, then either its endomorphism algebra is isomorphic to $D$, or $p > 0$ and $J(C)$ is a supersingular abelian variety. The supersingular outcome cannot occur when $p$ splits in $D$. | |
| dc.description | Corrected typos; clarified proofs; added more examples in positive characteristic | |
| dc.identifier | https://arxiv.org/abs/math/0403553 | |
| dc.identifier | http://arxiv.org/abs/math/0403553 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/70669 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 14H40; 14H15; 11G10 | |
| dc.title | Hyperelliptic jacobians with real multiplication | |
| dc.type | text |