On Families of (Phi,Gamma)-modules
Kedlaya, Kiran ; Liu, Ruochuan
arXiv, 0812.0112 / Harvested from arXiv
Text on arXiv
Berger and Colmez introduced a theory of families of overconvergent \'etale (Phi,Gamma)-modules associated to families of p-adic Galois representations over p-adic Banach algebras. However, in contrast with the classical theory of (Phi,Gamma)-modules, the functor they obtain is not an equivalence of categories. In this paper, we prove that when the base is an affinoid space, every family of (overconvergent) \'etale (Phi,Gamma)-modules can locally be converted into a family of p-adic representations in a unique manner, providing the "local" equivalence. There is a global mod p obstruction related to the moduli of residual representations.
Publié le : 2008-11-29
Classification:  Mathematics - Number Theory,  Mathematics - Algebraic Geometry,  11F 
@article{0812.0112,
     author = {Kedlaya, Kiran and Liu, Ruochuan},
     title = {On Families of (Phi,Gamma)-modules},
     journal = {arXiv},
     volume = {2008},
     number = {0},
     year = {2008},
     language = {en},
     url = {http://dml.mathdoc.fr/item/0812.0112}
}

Kedlaya, Kiran; Liu, Ruochuan. On Families of (Phi,Gamma)-modules. arXiv, Tome 2008 (2008) no. 0, . http://gdmltest.u-ga.fr/item/0812.0112/