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Classification of supersingular abelian varieties. (English) Zbl 0641.14008
After studying the structure of supersingular abelian crystals, we can construct the fine moduli spaces of supersingular abelian schemes with some “level structure”. Such a level structure can be recovered from the crystalline cohomology, and can be given to any family of supersingular abelian varieties after slight modification. Therefore supersingular abelian varieties of a given dimension are classified up to isomorphisms by a set of integer invariants (called an “index”) and a finite number of quasi-projective varieties, one for each index.
Reviewer: Li Kezheng

14F30 \(p\)-adic cohomology, crystalline cohomology
14K05 Algebraic theory of abelian varieties
14B05 Singularities in algebraic geometry
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