This is a joint seminar with algebra seminar.
A classical result of Fontaine-Colmez in p-adic Hodge theory says that one can classify crystalline representations of Galois groups of p-adic fields using certain semi-linear objects, namely the weakly admissible (filtered, phi)-modules. In this talk we propose a notion of (filtered, phi)-modules over smooth adic spaces over p-adic fields, and give a characterization of their admissible locus. That is the part of the base where one can convert the (filtered, phi)-modules to crystalline local systems. This generalizes the works of Fontaine-Colmez, Berger andBrinon, and the work of Hartl on admissible locus of period domains.