Let $k=\overline{k}$ be a field of characteristic $p$. Let $(K,\mathcal{O},k)$ be a $p$-modular system. Let both $k$ and $K$ be splitting fields for $G$ and its subgroups.
The ring $\mathcal{O}$ can have characteristic zero or characteristic $p$.
What is the difference? Which are important implications that follow in the first case but not in the latter one (and vice versa)?
I would be grateful for a book or another reference. Thank you.
