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On fields of definition of components of the Siegel supersingular locus


Author: Chia-Fu Yu
Journal: Proc. Amer. Math. Soc. 145 (2017), 5053-5058
MSC (2010): Primary 11G15, 11G10
DOI: https://doi.org/10.1090/proc/13741
Published electronically: August 30, 2017
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Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)

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Additional Information

Chia-Fu Yu
Affiliation: Institute of Mathematics, Academia Sinica, 6th Floor, Astronomy Mathematics Building, No. 1, Roosevelt Road Section 4, Taipei, Taiwan, 10617 – and – National Center for Theoretical Sciences, No. 1 Roosevelt Road Section 4, National Taiwan University, Taipei, Taiwan, 10617
Email: chiafu@math.sinica.edu.tw

DOI: https://doi.org/10.1090/proc/13741
Keywords: Superspecial abelian surfaces, supersingular locus, field of definition
Received by editor(s): December 5, 2016
Published electronically: August 30, 2017
Communicated by: Matthew A. Papanikolas
Article copyright: © Copyright 2017 American Mathematical Society