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 language||English (US)|
|Number of pages||11|
|Journal||Mathematical Proceedings of the Cambridge Philosophical Society|
|State||Published - Mar 2004|
All Science Journal Classification (ASJC) codes