Hypersymmetric Abelian Varieties
Ching-Li Chai, Frans Jeroen Oort · Pure and Applied Mathematics Quarterly · 2006
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.