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| Main Author: | |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2604.17059 |
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| _version_ | 1866910143673794560 |
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| author | Cheng, Haochen |
| author_facet | Cheng, Haochen |
| contents | We study families of abelian varieties over smooth proper curves with small $l$-adic local system over characteristic $p$. We show that such abelian schemes have a non-nef Hodge bundle and cannot be lifted to $W_2(k)$. We also establish an Arakelov-type inequality for families of abelian varieties over smooth proper curves in characteristic $p$, assuming $W_2(k)$-liftability. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_17059 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Non-liftability of Families of Abelian Varieties with Small $l$-adic Local System Cheng, Haochen Number Theory Algebraic Geometry We study families of abelian varieties over smooth proper curves with small $l$-adic local system over characteristic $p$. We show that such abelian schemes have a non-nef Hodge bundle and cannot be lifted to $W_2(k)$. We also establish an Arakelov-type inequality for families of abelian varieties over smooth proper curves in characteristic $p$, assuming $W_2(k)$-liftability. |
| title | Non-liftability of Families of Abelian Varieties with Small $l$-adic Local System |
| topic | Number Theory Algebraic Geometry |
| url | https://arxiv.org/abs/2604.17059 |