Showing papers on "Abelian category published in 1991"

Browder-livesay groups of abelian 2-groups

Abstract: The authors compute all the Browder-Livesay groups of an arbitrary finite abelian 2-group with an arbitrary orientation character and any subgroup of index 2. Browder-Livesay groups are obstruction groups for the problem of splitting homotopy equivalences of manifolds along one-sided submanifolds of codimension 1. All the connections with the Wall groups of abelian 2-groups which can be expressed by two-row diagrams are uncovered.

On the l-adic representations attached to simple abelian varieties of type IV

Abstract: The l-adic representations associated to prime dimensional type IV absolutely simple abelian varieties over number fields are studied. The image of such a representation was computed. The results coincide with the well-known conjectures of Mumford and Tate.

Radon-Nikodým properties associated with subsets of countable discrete abelian groups

Abstract: With any subset of a countable discrete abelian we associate with it three Banach space properties. These properties are Radon-Nikodym type properties. The relationship between these properties is investigated. The results are applied to give new characterizations of Riesz subsets and Rosenthal subsets of countable discrete abelian groups.

Abelian Varieties of K3 Type and ℓ-Adic Representations

Abstract: In this paper we study the algebraic envelopes of one-dimensional l-adic Lie algebras attached to the Galois actions on the Tate modules of Abelian varieties over finite fields. These envelopes are linear reductive commutative Lie algebras. We prove that these envelopes (after an extension of scalars) are generated by semisimple linear operators, whose spectrum coincides with the set of slopes of the Newton polygon of the Abelian variety. In addition, the multiplicity of each eigen value is equal to the length of the slope.