The endomorphism rings of jacobians of cyclic covers of the projective line
| dc.creator | Zarhin, Yuri G. | |
| dc.date | 2001-03-28 | |
| dc.date | 2002-09-08 | |
| dc.date.accessioned | 2026-07-07T04:40:49Z | |
| dc.date.available | 2026-07-07T04:40:49Z | |
| dc.description | Suppose K is a field of characteristic 0, $K_a$ is its algebraic closure, p is an odd prime. Suppose, $f(x) \in K[x]$ is a polynomial of degree $n \ge 5$ without multiple roots. Let us consider a curve $C: y^p=f(x)$ and its jacobian J(C). It is known that the ring End(J(C)) of all $K_a$-endomorphisms of J(C) contains the ring $Z[ζ_p]$ of integers in the pth cyclotomic field (generated by obvious automorphisms of C). We prove that $End(J(C))=Z[ζ_p]$ if the Galois group of f over K is either the symmetric group $S_n$ or the alternating group $A_n$. | |
| dc.description | LaTeX2e, 14 pages. The paper will appear in Math. Proc. Cambridge Philos. Soc | |
| dc.identifier | https://arxiv.org/abs/math/0103203 | |
| dc.identifier | http://arxiv.org/abs/math/0103203 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/61161 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | Number Theory | |
| dc.subject | 14H40; 14K15; 14C25 | |
| dc.title | The endomorphism rings of jacobians of cyclic covers of the projective line | |
| dc.type | text |