Faltings extension and Hodge-Tate filtration for abelian varieties over $p$-adic local fields with imperfect residue fields

Tongmu He

doi:10.4153/s0008439520000399

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arXiv · 2003.09687

Faltings extension and Hodge-Tate filtration for abelian varieties over $p$-adic local fields with imperfect residue fields

Tongmu He

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Abstract

Let $K$ be a complete discrete valuation field of characteristic $0$ with not necessarily perfect residue field of characteristic $p>0$. We define a Faltings extension of $\mathcal{O}_K$ over $\mathbb{Z}_p$, and we construct a Hodge-Tate filtration for abelian varieties over $K$ by generalizing Fontaine's construction in 1981, where he treated the perfect residue field case.

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Tongmu He. 2020-03-21. Faltings extension and Hodge-Tate filtration for abelian varieties over $p$-adic local fields with imperfect residue fields. https://doi.org/10.4153/s0008439520000399

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