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

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...

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Bibliographic Details
Published inCanadian mathematical bulletin Vol. 64; no. 2; pp. 247 - 263
Main Author He, Tongmu
Format Journal Article
LanguageEnglish
Published Canada Canadian Mathematical Society 01.06.2021
Cambridge University Press
Subjects
Algebra
Decomposition
Filtration
Residues
Valuation
imperfect residue field
Hodge-Tate
14K15
14G20
14F30
p-adic
Faltings extension
abelian variety
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Summary: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.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:0008-4395
1496-4287
DOI:10.4153/S0008439520000399