Endomorphisms of superelliptic jacobians

Endomorphisms of Superelliptic Jacobians

Let K be a field of characteristic zero, n ≥ 5 an integer, f(x) an irreducible polynomial over K of degree n, whose Galois group contains a doubly transitive simple non-abelian group. Let p be an odd prime, Z[ζp] the ring of integers in the pth cyclotomic field, Cf,p : y p = f(x) the corresponding superelliptic curve and J(Cf,p) its jacobian. Assuming that either n = p + 1 or p does not divide ...

Non-isogenous Superelliptic Jacobians

Let p be an odd prime. Let K be a field of characteristic zero and Ka its algebraic closure. Let n ≥ 5 and m ≥ 5 be integers. Let f(x), h(x) ∈ K[x] be irreducible separable polynomials of degree n and m respectively. Suppose that the Galois group of f is either the full symmetric group Sn or the alternating group An and the Galois group of h is either the full symmetric group Sm or the alternat...

Endomorphism Algebras of Superelliptic Jacobians

As usual, we write Z,Q,Fp,C for the ring of integers, the field of rational numbers, the finite field with p elements and the field of complex numbers respectively. If Z is a smooth algebraic variety over an algebraically closed field then we write Ω(Z) for the space of differentials of the first kind on Z. If Z is an abelian variety then we write End(Z) for its ring of (absolute) endomorphisms...

Centers of Hodge Groups of Superelliptic Jacobians

is surjective. If W is a Q-vector space, Q-algebra or Q-Lie algebra then we write WC for the correspondingC-vector space (respectively, C-algebra orC-Lie algebra) W ⊗Q C. Let f(x) ∈ C[x] be a polynomial of degree n ≥ 2 without multiple roots. Suppose that p is a prime that does not divide n and a positive integer q = p is a power of p. As usual, φ(q) = (p − 1)p denotes the Euler function. Let u...

Endomorphisms of Jacobians of Modular Curves