Torsion of Abelian varieties over GL (2)-extensions of number fields.
Abelian varieties over fields of finite characteristic
The aim of this paper is to extend our previous results about Galois action on the torsion points of abelian varieties to the case of (finitely generated) fields of characteristic 2.
Endomorphism algebras of complex tori.
Ordinary reduction of K3 surfaces
Let X be a K3 surface over a number field K. We prove that there exists a finite algebraic field extension E/K such that X has ordinary reduction at every non-archimedean place of E outside a density zero set of places.
Non-supersingular hyperelliptic jacobians
Let be a field of odd characteristic , let be an irreducible separable polynomial of degree with big Galois group (the symmetric group or the alternating group). Let be the hyperelliptic curve and its jacobian. We prove that does not have nontrivial endomorphisms over an algebraic closure of if either or .
Editorial Material
Semistable reduction and torsion subgroups of abelian varieties
The main result of this paper implies that if an abelian variety over a field has a maximal isotropic subgroup of -torsion points all of which are defined over , and , then the abelian variety has semistable reduction away from . This result can be viewed as an extension of Raynaud’s theorem that if an abelian variety and all its -torsion points are defined over a field and , then the abelian variety has semistable reduction away from . We also give information about the Néron models...
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