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Faltings extension and Hodge-Tate filtration for abelian varieties over p-adic local fields with imperfect residue fields
Published online by Cambridge University Press: 11 June 2020
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.
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- © Canadian Mathematical Society 2020
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