Endomorphisms of superelliptic jacobians

Abstract

Let K be a field of characteristic zero, n>4 an integer, f(x) an irreducible polynomial over K of degree n, whose Galois group is doubly transitive simple non-abelian group. Let p be an odd prime, Z[ζ_p] the ring of integers in the p-th cyclotomic field, C_{f,p}:y^p=f(x) the corresponding superelliptic curve and J(C_{f,p}) its jacobian. Assuming that either n=p+1 or p does not divide n(n-1), we prove that the ring of all endomorphisms of J(C_{f,p}) coincides with Z[ζ_p].

Several typos have been corrected

References in corpus (5)

• Very simple 2-adic representations and hyperelliptic jacobians
• Homomorphisms of hyperelliptic jacobians
• Homomorphisms of abelian varieties
• Superelliptic jacobians
• Endomorphism algebras of hyperelliptic jacobians and finite projective lines

Cited by in corpus (1)

• Families of explicitly isogenous Jacobians of variable-separated curves