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Friedlander and Mazur proposed a conjecture of hard Lefschetz type for Lawson homology. We shall relate this conjecture to Suslin's conjecture for Lawson homology and hence to Grothendieck's standard conjectures. Applying theSL2-action on abelian varieties observed by Beauville, we show that for abelian varieties, this conjecture is equivalent to a weak form of a vanishing conjecture of Beauville type for Lawson homology. [ABSTRACT FROM AUTHOR]

Using the categorical equivalence of the class of generalized MV-algebras with the class of unital ℓ-groups, we describe all varieties of symmetric top abelian unital ℓ-groups that cover the variety Auℓ of abelian unital ℓ-groups. Equivalently, we describe all cover varieties of the variety of MV-algebras, MV, within the variety of generalized MV-algebras admitting only one negation and each of whose maximal ideals is normal. In particular, there are continuum many representable varieties of generalized MV-algebras that cover MV. [ABSTRACT FROM AUTHOR]