I know that the p-adic representaions from geometries are de Rham representations and hence they are Hodge-Tate 
representations. Then, are there (more than 2-dimensional) Hodge-Tate representations not coming from geometries? If there are, let me know 
the references. Sorry if it is trivial.



Hodge-Tate representations
Every de Rham representation is Hodge--Tate, but the converse is not true -- there are Hodge--Tate representations which are not de Rham, and thus cannot appear in geometry. (Examples of these arise in dimension 2 via the theory of p-adic modular forms.)


I don't think anyone knows how to characterise, even conjecturally, the p-adic Galois representations of a p-adic field which come from geometry; there is a precise conjecture for Galois representations of number fields, due to Fontaine and Mazur, but as yet this has no local analogue.


