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

Part of: (Co)homology theory Abelian varieties and schemes Arithmetic problems. Diophantine geometry

Published online by Cambridge University Press:  11 June 2020

Tongmu He
Tongmu He*
Affiliation:
Institut des Hautes Études Scientifiques, 35 route de Chartres, 91440Bures-sur-Yvette, France
*
e-mail: hetm15@ihes.fr
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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 [Fon82] where he treated the perfect residue field case.

Keywords

Hodge-TateFaltings extensionabelian varietyp-adicimperfect residue field

MSC classification

Primary: 14F30: $p$-adic cohomology, crystalline cohomology
Secondary: 14G20: Local ground fields 14K15: Arithmetic ground fields
Type
Article
Information
Canadian Mathematical Bulletin , Volume 64 , Issue 2 , June 2021 , pp. 247 - 263
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Copyright
© Canadian Mathematical Society 2020

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