The endomorphism rings of jacobians of cyclic covers of the projective line

dc.creatorZarhin, Yuri G.
dc.date2001-03-28
dc.date2002-09-08
dc.date.accessioned2026-07-07T04:40:49Z
dc.date.available2026-07-07T04:40:49Z
dc.descriptionSuppose 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.descriptionLaTeX2e, 14 pages. The paper will appear in Math. Proc. Cambridge Philos. Soc
dc.identifierhttps://arxiv.org/abs/math/0103203
dc.identifierhttp://arxiv.org/abs/math/0103203
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/61161
dc.subjectAlgebraic Geometry
dc.subjectNumber Theory
dc.subject14H40; 14K15; 14C25
dc.titleThe endomorphism rings of jacobians of cyclic covers of the projective line
dc.typetext

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