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We study the special fibers of a certain class of absolutely simple abelianvarieties over number fields with endomorphism rings $\bz$ and possessing$l$-adic monodromy groups of the least possible rank. We also study theDirichlet density of the places at which the possible reductions occur andconfirm a special case of a broader conjecture for the splitting of reductionsof abelian varieties over number fields.

Reductions of abelian varieties of generalized Mumford type