Cyclic covers of prime power degree, jacobians and endomorphisms
| dc.creator | Zarhin, Yuri G. | |
| dc.date | 2003-12-27 | |
| dc.date.accessioned | 2026-07-07T05:04:13Z | |
| dc.date.available | 2026-07-07T05:04:13Z | |
| dc.description | Suppose that $K$ is a field of characteristic 0, $K_a$ is its algebraic closure, $p$ is a prime, $q=p^r$ is a power prime. Suppose that $f(x) \in K[x]$ is a polynomial of degree $n > 4$ without multiple roots. Let us consider the superelliptic curve $C: y^q=f(x)$ and its jacobian $J(C)$. We study the endomorphism algebra $End^0(J(C))$ of all $K_a$-endomorphisms of $J(C)$. We prove that $End^0(J(C))$ is "as small as possible" if the Galois group of $f$ over $K$ is either the full symmetric group $S_n$ or the alternating group $A_n$. | |
| dc.description | 33 pages, LaTeX2e | |
| dc.identifier | https://arxiv.org/abs/math/0312471 | |
| dc.identifier | http://arxiv.org/abs/math/0312471 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/69719 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | Number Theory | |
| dc.subject | 14H40; 14K05, 11G30 | |
| dc.title | Cyclic covers of prime power degree, jacobians and endomorphisms | |
| dc.type | text |