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Oort's conjecture for split unitary Shimura varieties
Abstract
We prove that generically on the basic stratum of split unitary Shimura varieties, the universal abelian variety with endomorphism structure and polarization has minimal automorphism group in a precise sense, except for a few degenerate cases. This is a direct analogue of Oort's conjecture on automorphisms of supersingular abelian varieties. On the way, we explicitly compute the generic automorphism group of the universal p-divisible group in a given basic isogeny class.
Related
- Ekedahl-Oort strata with a superspecial factor in unitary Shimura varieties
- Heights of small CM cycles on Unitary Shimura Varieties
- Modular Heights of Unitary Shimura Varieties II: Arithmetic Generating Series of Divisors
- Modular Heights of Unitary Shimura Varieties III: Proof of the Main Theorem
- On the singularities and the Kodaira dimension of unitary Shimura varieties
BibTeX
@misc{philippe2026oorts,
title = {{Oort's conjecture for split unitary Shimura varieties}},
author = {Paul Philippe and Fabian Schnelle and Eva Viehmann},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.04072},
eprint = {2609.04072},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.04072},
}
RIS
TY - UNPB
TI - Oort's conjecture for split unitary Shimura varieties
AU - Paul Philippe
AU - Fabian Schnelle
AU - Eva Viehmann
PY - 2026
DA - 2026/09/29
PB - arXiv
DO - 10.48550/arxiv.2609.04072
UR - https://arxiv.org/abs/2609.04072
AB - We prove that generically on the basic stratum of split unitary Shimura varieties, the universal abelian variety with endomorphism structure and polarization has minimal automorphism group in a precise sense, except for a few degenerate cases. This is a direct analogue of Oort's conjecture on automorphisms of supersingular abelian varieties. On the way, we explicitly compute the generic automorphism group of the universal p-divisible group in a given basic isogeny class.
ER -