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

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.

12 pages; to appear in Canadian Mathematical Bulletin

References in corpus (1)

• Les suites spectrales de Hodge-Tate

Cited by in corpus (2)

• Sen Operators and Lie Algebras arising from Galois Representations over $p$-adic Varieties
• Perfectoidness via Sen Theory and Applications to Shimura Varieties