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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

Tongmu He*
Institut des Hautes Études Scientifiques, 35 route de Chartres, 91440Bures-sur-Yvette, France


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.

© Canadian Mathematical Society 2020

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