Throughout this paper K is a field of characteristic 6= 2 and Ka its algebraic closure. If f(x) ∈ K[x] is a separable polynomial of degree n ≥ 5 then it gives rise to the hyperelliptic curve C = Cf :… (More)

ζp ∈ C. Let Q(ζp) be the pth cyclotomic field. It is well-known that Q(ζp) is a CM-field. If p is a Fermat prime then the only CM-subfield of Q(ζp) is Q(ζp) itself, since the Galois group of Q(ζp)/Q… (More)

has only trivial endomorphisms over an algebraic closure of the ground field K if the Galois group Gal(f) of the polynomial f ∈ K[x] is “very big”. More precisely, if f is a polynomial of degree n ≥… (More)

Throughout the paper we will freely use the following observation [21, p. 174]: if an abelian variety X is isogenous to a self-product Z of an abelian variety Z then a choice of an isogeny between X… (More)

We obtain an easy sufficient condition for the Brauer group of a diagonal quartic surface D over Q to be algebraic. We also give an upper bound for the order of the quotient of the Brauer group of D… (More)

has only trivial endomorphisms over an algebraic closure of the ground field K if the Galois group Gal(f) of the polynomial f ∈ K[x] of even degree is “very big”. More precisely, if f is a polynomial… (More)

In [17] the author proved that in characteristic 0 the jacobian J(C) = J(Cf ) of a hyperelliptic curve C = Cf : y 2 = f(x) has only trivial endomorphisms over an algebraic closure Ka of the ground… (More)

Let K be a field with char(K) 6= 2. Let us fix an algebraic closure Ka of K. Let us put Gal(K) := Aut(Ka/K). If X is an abelian variety of positive dimension over Ka then we write End(X) for the ring… (More)

As usual, Z, Q and C stand for the ring of integers, the field of rational numbers and the field of complex numbers respectively. If l is a prime then we write Fl,Zl and Ql for the l-element (finite)… (More)