Everett W. Howe: Kernels of polarizations of abelian varieties over finite fields, J. Algebraic Geom. 5 (1996) 583–608, MR 96m:14063, Zbl 0911.11031.
A preprint version of the paper is available here. Unfortunately, the Journal of Algebraic Geometry does not provide access to digital versions of any paper it published before 2002.
In this paper I succeed in removing the ‘ordinary’ hypothesis from the major results in my thesis. In particular, I show that every simple odd-dimensional abelian variety over a finite field is isogenous to a principally polarized variety. To do this I need to investigate the Grothendieck group of the category of kernels of isogenies between elements of a given isogeny class. I also have to prove results on reduced norms in central simple algebras over number fields, results that can be viewed as extensions of the Hasse-Schilling-Maass theorem.