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Every ordinary symplectic isogeny class in positive characteristic is dense in the moduli. (English) Zbl 0990.11039
From the text: We prove that any ordinary symplectic separable isogeny class in the moduli space of principally polarized abelian varieties over a field of positive characteristic is dense in the Zariski topology.
Contents: Sect. 1. Strategy and methods of the proof; Sect. 2. Calculation at the 0-dimensional cusp; Sect. 3. Reduction to the Hilbert-Blumenthal case; Sect. 4. Calculation of smooth ordinary points over finite fields; Sect. 5. Inspection at the supersingular points.

MSC:
11G10 Abelian varieties of dimension \(> 1\)
14K15 Arithmetic ground fields for abelian varieties
11G25 Varieties over finite and local fields
14G20 Local ground fields in algebraic geometry
14K10 Algebraic moduli of abelian varieties, classification
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