Lattices in crystalline representations and Kisin modules associated with iterate extensions

Abstract

Cais and Liu extended the theory of Kisin modules and crystalline representations to allow more general coefficient fields and lifts of Frobenius. Based on their theory, we classify lattices in crystalline representations by Kisin modules with additional structures under a Cais-Liu's setting. Furthermore, we give a geometric interpretation of Kisin modules of height one in terms of Dieudonné crystals of $p$-divisible groups, and show a full faithfulness theorem for a restriction functor on torsion crystalline representations.

35 pages, some minor modifications, new results were added in the final section

References in corpus (2)

• Group schemes of period 2
• On F-crystalline representations

Cited by in corpus (3)

• Moduli stacks of étale (phi,Gamma)-modules and the existence of crystalline lifts
• Crystalline condition for $A_{\inf }$-cohomology and ramification bounds
• A prismatic approach to $(\phi ,\hat{G})$-modules and $F$-crystals