Geodesic
On $F$-crystalline representations
Documenta mathematica, Tome 21 (2016), pp. 223-270
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We extend the theory of Kisin modules and crystalline representations to allow more general coefficient fields and lifts of Frobenius. In particular, for a finite and totally ramified extension F/Qp​, and an arbitrary finite extension K/F, we construct a general class of infinite and totally wildly ramified extensions K∞​/K so that the functor V↦V∣GK∞​​​ is fully-faithfull on the category of F-crystalline representations V. We also establish a new classification of F-Barsotti–Tate groups via Kisin modules of height 1 which allows more general lifts of Frobenius.
DOI : 10.4171/dm/532
Classification : 14F30, 14L05
Mots-clés : F-crystalline representations, kisin modules 
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     author = {Bryden Cais and Tong Liu},
     title = {On $F$-crystalline representations},
     journal = {Documenta mathematica},
     pages = {223--270},
     year = {2016},
     volume = {21},
     doi = {10.4171/dm/532},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/532/}
}
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Bryden Cais; Tong Liu. On $F$-crystalline representations. Documenta mathematica, Tome 21 (2016), pp. 223-270. doi: 10.4171/dm/532

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