TY - JOUR
T1 - The endomorphism rings of jacobians of cyclic covers of the projective line
AU - Zarhin, Yuri G.
PY - 2004/3
Y1 - 2004/3
N2 - 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].
AB - 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].
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U2 - 10.1017/S0305004103007102
DO - 10.1017/S0305004103007102
M3 - Article
AN - SCOPUS:1642586829
SN - 0305-0041
VL - 136
SP - 257
EP - 267
JO - Mathematical Proceedings of the Cambridge Philosophical Society
JF - Mathematical Proceedings of the Cambridge Philosophical Society
IS - 2
ER -