Representations over $\mathbb{Q}_p$ I would like to understand representations over the $p$-adic field $\mathbb{Q}_p$ and find simple $\mathbb{Q}_p[G]$ modules for a finite group $G$. Is there some famous literature like for representations over $\mathbb{Z}$ from Curtis and Reiner? Especially I am looking for theorems with tells something about the number of simple $\mathbb{Q}_p[G]$ modules.
Thank you for hints
 A: If $F$ is any field of char. zero, then $F[G]$ is a semisimple algebra, and general Wedderburn theory applies.  
If we extend scalars to $\overline{F}$ (an alg. closure of $F$) then $\overline{F}[G]$ is a product of matrix rings over $\overline{F}$, and doesn't depend on which algebraically closed field you choose.  
If $F$ is not algebraically closed, then $F[G]$ will be a product of matrix rings over division rings over $F$, and which ones appear depend on the details of the group $G$ and the field $F$ (basically, it depends on what algebraic integers do or don't already lie in $F$).  
This should be explained in any reasonable text on group reps. (If you look up ``Schur index'' in the index of the book, this should take you to the section where non-algebraically closed fields are considered.)
In the case of $\mathbb Q_p$, there is a good theory of division rings over $p$-adic fields (part of local class field theory), and this will likely be a useful tool.  
The analogy with $\mathbb Z[G]$ is not very good, because there the main point is that $\mathbb Z$ is not a field, so $\mathbb Z[G]$ is an order in a semisimple ring , rather than a semisimple ring itself.
