Abelian varieties with real multiplication: Classification and isogeny classes over finite fields
Creators
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1.
The Ohio State University
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2.
California Institute of Technology
Abstract
In this paper, we provide a classification of certain points on Hilbert modular varieties over finite fields under a mild assumption on Newton polygon. Furthermore, we use this characterization to prove estimates for the size of isogeny classes.
Copyright and License
© 2025 Elsevier Inc. All rights are reserved, including those for text and data mining, AI training, and similar technologies.
Acknowledgement
Our approach owes a substantial intellectual debt to the work of Oswal and Shankar. We are very grateful to Ananth Shankar for introducing this question to us and for his help throughout the project. We wish to thank Nathan Kaplan and Ziquan Yang for helpful conversations. We thank Jordan Ellenberg for many useful comments on the introduction. Finally, we thank the referee for the comments that greatly improved the exposition of the paper.
Funding
We were partially supported by NSF grant DMS-2100436.
Additional details
Related works
- Is new version of
- Discussion Paper: arXiv:2308.11105 (arXiv)
Funding
- National Science Foundation
- DMS-2100436
Dates
- Accepted
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2025-08-12
- Available
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2025-09-05Available online
- Available
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2025-09-16Version of record