Traverso's Isogeny Conjecture for Some Unitary p-Divisible Groups
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| Main Authors: | , , , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866918104756387840 |
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| author | Andrews, Emerald Bhamidipati, Deewang Fox, Maria Goodson, Heidi Groen, Steven R. Nair, Sandra |
| author_facet | Andrews, Emerald Bhamidipati, Deewang Fox, Maria Goodson, Heidi Groen, Steven R. Nair, Sandra |
| contents | The isogeny cutoff of a $p$-divisible group $X$ (defined over an algebraically closed field of characteristic $p$) measures the amount of $p$-torsion necessary to determine its isogeny class. The minimal height of $X$ measures its distance to the closest minimal $p$-divisible group (in the sense of Oort). In this paper, we study these invariants for supersingular unitary $p$-divisible groups of signature $(a,b)$. We provide a complete description of the possible minimal heights. As an application, we establish bounds on the isogeny cutoffs for these $p$-divisible groups. Finally, we rephrase our results in the language of the $\mathrm{BT}_m$ stratifications of unitary Shimura varieties of signature $(a,b)$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2507_19708 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Traverso's Isogeny Conjecture for Some Unitary p-Divisible Groups Andrews, Emerald Bhamidipati, Deewang Fox, Maria Goodson, Heidi Groen, Steven R. Nair, Sandra Number Theory Algebraic Geometry 14L05, 11G18, 11G10 The isogeny cutoff of a $p$-divisible group $X$ (defined over an algebraically closed field of characteristic $p$) measures the amount of $p$-torsion necessary to determine its isogeny class. The minimal height of $X$ measures its distance to the closest minimal $p$-divisible group (in the sense of Oort). In this paper, we study these invariants for supersingular unitary $p$-divisible groups of signature $(a,b)$. We provide a complete description of the possible minimal heights. As an application, we establish bounds on the isogeny cutoffs for these $p$-divisible groups. Finally, we rephrase our results in the language of the $\mathrm{BT}_m$ stratifications of unitary Shimura varieties of signature $(a,b)$. |
| title | Traverso's Isogeny Conjecture for Some Unitary p-Divisible Groups |
| topic | Number Theory Algebraic Geometry 14L05, 11G18, 11G10 |
| url | https://arxiv.org/abs/2507.19708 |