Abstract
We introduce the notion of a hypersymmetric abelian variety over a field of positive characteristic p. We show that every symmetric Newton polygon admits a hypersymmetric abelian variety having that Newton polygon; see 2.5 and 4.8. Isogeny classes of absolutely simple hypersymmetric abelian varieties are classified in terms of their endomorphism algebras and Newton polygons. We also discuss connections with abelian varieties of PEL-type, i.e. abelian varieties with extra symmetries, especially abelian varieties with real multiplications.
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