Mass formula and Oort's conjecture for supersingular abelian threefolds

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Mass formula and Oort's conjecture for supersingular abelian threefolds
 
Karemaker, Valentijn; Yobuko, Fuetaro; Yu, Chia-Fu
(2021) Advances in Mathematics, volume 386
(Article)
Abstract
Katsura and Oort obtained an explicit description of the supersingular locus S3,1 of the Siegel modular variety of degree 3 in terms of class numbers. In this paper we study an alternative stratification of S3,1, the so-called mass stratification. We show that when p = 2, there are eleven strata ... read more
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Keywords: Automorphism groups, Mass formulae, Supersingular abelian varieties, Taverne, General Mathematics
DOI: https://doi.org/10.1016/j.aim.2021.107812
ISSN: 0001-8708
Publisher: Academic Press Inc.
Note: Funding Information: Parts of this work were carried out when the first author visited the Academia Sinica, and when the first and third authors visited RIMS and Kyoto University. They would like to thank these institutes for their hospitality and excellent working conditions. A part of this paper is contained in the second author's master's thesis written at Tohoku University; he thanks his advisor Nobuo Tsuzuki for enlightening comments, advice and encouragement. The authors are grateful to Ming-Lun Hsieh and Akio Tamagawa for useful discussions, and for proving Propositions A.2 and A.3, respectively. They would like to thank Tomoyoshi Ibukiyama and Jiangwei Xue for useful discussions and helpful comments on an earlier manuscript, and the anonymous referee for their comments which improved the exposition. The second author is supported by JSPS grants 15J05073 and 19K14501. The third author is partially supported by MoST grants 107-2115-M-001-001-MY2 and 109-2115-M-001-002-MY3. Funding Information: Parts of this work were carried out when the first author visited the Academia Sinica, and when the first and third authors visited RIMS and Kyoto University. They would like to thank these institutes for their hospitality and excellent working conditions. A part of this paper is contained in the second author's master's thesis written at Tohoku University; he thanks his advisor Nobuo Tsuzuki for enlightening comments, advice and encouragement. The authors are grateful to Ming-Lun Hsieh and Akio Tamagawa for useful discussions, and for proving Propositions A.2 and A.3 , respectively. They would like to thank Tomoyoshi Ibukiyama and Jiangwei Xue for useful discussions and helpful comments on an earlier manuscript, and the anonymous referee for their comments which improved the exposition. The second author is supported by JSPS grants 15J05073 and 19K14501 . The third author is partially supported by MoST grants 107-2115-M-001-001-MY2 and 109-2115-M-001-002-MY3 . Publisher Copyright: © 2021 Elsevier Inc.
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