Cyclic covers of the projective line, their jacobians and endomorphisms
| dc.creator | Zarhin, Yuri G. | |
| dc.date | 2000-08-16 | |
| dc.date | 2001-03-13 | |
| dc.date.accessioned | 2026-07-07T04:36:51Z | |
| dc.date.available | 2026-07-07T04:36:51Z | |
| dc.description | We study the endomorphism ring $End(J(C))$ of the complex jacobian $J(C)$ of a curve $y^p=f(x)$ where $p$ is an odd prime and $f(x)$ is a polynomial with complex coefficiens of degree $n>4$ and without multiple roots. Assume that all the coefficients of $f$ lie in a (sub)field $K$ and the Galois group of $f$ over $K$ is either the full symmetric group $S_n$ or the alternating group $A_n$. Then we prove that $End(J(C))$ is the ring of integers in the in the $p$th cyclotomic field, if $p$ is a Fermat prime (e.g., $p=3,5,17,257$). Similar results for $p=2$ (the case of hyperelliptic curves) were obtained by the author in Math. Res. Lett. 7(2000), 123--132. | |
| dc.description | LaTeX2e, 17 pages Some typos were corrected | |
| dc.identifier | https://arxiv.org/abs/math/0008134 | |
| dc.identifier | http://arxiv.org/abs/math/0008134 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/59754 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | Number Theory | |
| dc.subject | 14H40; 14K15; 14C25 | |
| dc.title | Cyclic covers of the projective line, their jacobians and endomorphisms | |
| dc.type | text |