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

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Abstract

Suppose that K is a field of characteristic zero, Ka is its algebraic closure, and that f(x) ∈ K[x] is an irreducible polynomial of degree n ≥ 5, whose Galois group coincides either with the full symmetric group An or with the alternating group An. Let p be an odd prime, Z[ζp] the ring of integers in the pth cyclotomic field Q(ζp). Suppose that C is the smooth projective model of the affine curve yp = f(x) and J(C) is the jacobian of C. We prove that the ring End(J((C)) of Ka-endomorphisms of J(C) is canonically isomorphic to Z[ζP].

Original languageEnglish (US)
Pages (from-to)257-267
Number of pages11
JournalMathematical Proceedings of the Cambridge Philosophical Society
Volume136
Issue number2
DOIs
StatePublished - Mar 2004

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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