Skip to content
DraconiticResearch
Search Sources API
189,280 studies31 sourcesUpdated 34 min ago
PreprintCC BY-NC-SA 4.0arXiv

Ekedahl-Oort strata with a superspecial factor in unitary Shimura varieties

  • Emerald Andrews
  • Deewang Bhamidipati
  • Heidi Goodson
  • Steven R. Groen
  • Sandra Nair
Open at sourcePDFDOICite

Abstract

Let k be an algebraically closed field of characteristic p>2 and let OK be an imaginary quadratic order in which p is inert. For any a,b∈ ℤ≥ 0 not both 0, denote by M(a,b) the unitary Shimura variety that parametrizes principally polarized abelian varieties over k with an action of signature (a,b) by OK (subject to certain compatibility conditions). For any a,b,c,d ∈ ℤ≥ 0, there is a natural product map M(a,b) × M(c,d) → M(a+c,b+d), which induces a map on Ekedahl-Oort strata. In this paper we focus on product maps where at least one of the factors is superspecial, since most Ekedahl-Oort strata of unitary Shimura varieties contain such a factor. We describe maps with this property completely on the level of Weyl group coset representatives. We also characterize, on the level of Weyl group coset representatives, which Ekedahl-Oort strata of M(a,b) admit a superspecial factor.

Related

  1. Stable Trace Formula for Newton strata of Shimura varieties
    Dhruva Kelkar
    arXivPreprintCC BY 4.0Full textAlgebra & number theoryarXiv
  2. Heights of small CM cycles on Unitary Shimura Varieties
    Ziqi Guo
    arXivPreprintarXiv licenceFull textAlgebra & number theoryarXiv
  3. Oort's conjecture for split unitary Shimura varieties
    Paul Philippe, Fabian Schnelle, Eva Viehmann
    arXivPreprintarXiv licenceFull textAlgebra & number theoryarXiv
  4. Modular Heights of Unitary Shimura Varieties II: Arithmetic Generating Series of Divisors
    Ziqi Guo
    arXivPreprintarXiv licenceFull textAlgebra & number theoryarXiv
  5. Modular Heights of Unitary Shimura Varieties III: Proof of the Main Theorem
    Ziqi Guo
    arXivPreprintarXiv licenceFull textAlgebra & number theoryarXiv

Cite

BibTeXRIS
BibTeX
@misc{andrews2026ekedahloort,
  title = {{Ekedahl-Oort strata with a superspecial factor in unitary Shimura varieties}},
  author = {Emerald Andrews and Deewang Bhamidipati and Heidi Goodson and Steven R. Groen and Sandra Nair},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.22036},
  eprint = {2610.22036},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.22036},
  note = {CC BY-NC-SA 4.0},
}
RIS
TY  - UNPB
TI  - Ekedahl-Oort strata with a superspecial factor in unitary Shimura varieties
AU  - Emerald Andrews
AU  - Deewang Bhamidipati
AU  - Heidi Goodson
AU  - Steven R. Groen
AU  - Sandra Nair
PY  - 2026
DA  - 2026/10/15
PB  - arXiv
DO  - 10.48550/arxiv.2610.22036
UR  - https://arxiv.org/abs/2610.22036
AB  - Let k be an algebraically closed field of characteristic p>2 and let O_K be an imaginary quadratic order in which p is inert. For any a,b∈ ℤ_≥ 0 not both 0, denote by M(a,b) the unitary Shimura variety that parametrizes principally polarized abelian varieties over k with an action of signature (a,b) by O_K (subject to certain compatibility conditions). For any a,b,c,d ∈ ℤ_≥ 0, there is a natural product map M(a,b) × M(c,d) → M(a+c,b+d), which induces a map on Ekedahl-Oort strata. In this paper we focus on product maps where at least one of the factors is superspecial, since most Ekedahl-Oort strata of unitary Shimura varieties contain such a factor. We describe maps with this property completely on the level of Weyl group coset representatives. We also characterize, on the level of Weyl group coset representatives, which Ekedahl-Oort strata of M(a,b) admit a superspecial factor.
ER  -