On fields of definition of components of the Siegel supersingular locus

Yu, Chia-Fu

doi:10.1090/proc/13741

On fields of definition of components of the Siegel supersingular locus
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Proc. Amer. Math. Soc. 145 (2017), 5053-5058 Request permission

Abstract:

Recently Ibukiyama proved an explicit formula for the number of certain non-principal polarizations on a superspecial abelian surface, extending his earlier work with Katsura for principal polarizations [Compos. Math. 91 (1994), 37–46]. As a consequence of Ibukiyama’s formula, there exists a geometrically irreducible component of the Siegel supersingular locus which is defined over the prime finite field. In this note we give a direct proof of this result.

References

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