Abstract
We describe the intersection of the Torelli locus j(Mct4 )=J4 with Newton and Ekedahl-Oort strata related to the supersingular locus in characteristic 2. We show that the locus of supersingular Jacobians S4 ∩ J4 in characteristic 2 is pure of dimension three. One way to obtain that result uses an analysis of the data of smooth genus four curves and principally polarized abelian fourfolds defined over F2, and another involves a more careful study of some relevant Ekedahl-Oort loci.
Original language | English |
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Pages (from-to) | 2333-2347 |
Number of pages | 15 |
Journal | Proceedings of the American Mathematical Society |
Volume | 152 |
Issue number | 6 |
Early online date | 12 Apr 2024 |
DOIs | |
Publication status | Published - 12 Apr 2024 |
Bibliographical note
Publisher Copyright:©2024 American Mathematical Society.
Funding
Received by the editors June 14, 2023, and, in revised form, September 29, 2023, October 24, 2023, and November 3, 2023. 2020 Mathematics Subject Classification. Primary 14H10, 14H40, 11G20, 11G10, 11M38. Key words and phrases. Supersingular, curves, genus four, Jacobians, finite fields, Ekedahl-Oort types. The author was supported by the Mathematical Institute of Utrecht University.
Funders | Funder number |
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Mathematical Institute of Utrecht University |
Keywords
- EkedahlOort types
- Jacobians
- Supersingular
- Curves
- Finite fields
- Genus four
- finite fields
- curves
- Ekedahl-Oort types
- genus four