Hyperelliptic jacobians without complex multiplication and Steinberg representations in positive characteristic
| dc.creator | Zarhin, Yuri G. | |
| dc.date | 2003-01-16 | |
| dc.date | 2003-11-09 | |
| dc.date.accessioned | 2026-07-07T04:54:29Z | |
| dc.date.available | 2026-07-07T04:54:29Z | |
| dc.description | In his previous papers (Math. Res. Letters 7 (2000), 123--13; Math. Res. Letters 8 (2001), 429--435; Moscow Math. J. 2 (2002), issue 2, 403-431) the author proved that in characteristic $\ne 2$ the jacobian $J(C)$ of a hyperelliptic curve $C: y^2=f(x)$ has only trivial endomorphisms over an algebraic closure $K_a$ of the ground field $K$ if the Galois group $\Gal(f)$ of the irreducible polynomial $f(x) \in K[x]$ is either the symmetric group $\Sn$ or the alternating group $\A_n$. Here $n\ge 9$ is the degree of $f$. The goal of this paper is to extend this result to the case of certain ``smaller'' doubly transitive simple Galois groups. Namely, we treat the infinite series $n=2^m+1, \Gal(f)=Ł_2(2^m):=\PSL_2(\F_{2^m})$, $n=2^{4m+2}+1, \Gal(f)=\Sz(2^{2m+1})= {^2\B_2}(2^{2m+1})$ and $n=2^{3m}+1, \Gal(f)=\U_3(2^m):=\PSU_3(\F_{2^m})$. | |
| dc.description | LaTeX2e, 11 pages | |
| dc.identifier | https://arxiv.org/abs/math/0301177 | |
| dc.identifier | http://arxiv.org/abs/math/0301177 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/66272 | |
| dc.subject | Number Theory | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 14H40;14K05 | |
| dc.title | Hyperelliptic jacobians without complex multiplication and Steinberg representations in positive characteristic | |
| dc.type | text |