Hodge groups of certain superelliptic jacobians
نویسندگان
چکیده
منابع مشابه
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...
متن کاملEndomorphisms 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 ...
متن کاملNon-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...
متن کاملEndomorphism 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...
متن کاملHodge Groups of Hodge Structures with Hodge Numbers
This paper studies the possible Hodge groups of simple polarizable Q-Hodge structures with Hodge numbers (n, 0, . . . , 0, n). In particular, it generalizes earlier work of Ribet and MoonenZarhin to completely determine the possible Hodge groups of such Hodge structures when n is equal to 1, 4, or a prime p. In addition, the paper determines possible Hodge groups, under certain conditions on th...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Mathematical Research Letters
سال: 2010
ISSN: 1073-2780,1945-001X
DOI: 10.4310/mrl.2010.v17.n2.a15