You might want to try tilting modules. Those at least provide a generating set with trivial self-extensions.

You might want to try tilting modules. Those at least provide a generating set with trivial self-extensions.

If I recall correctly, each tilting is left and right orthogonal to all but finitely many simples, and vice-versa, and every finite-dimensional module has a finite-length tilting resolution.

That is, the derived category of finite-dimensional modular representations is derived equivalent to bounded, finite rank perfect complexes over the endomorphism ring of the tiltings.

don't the simple modules (or Weyl modules, or tilting modules) generate? am I missing something subtle about the fact that you're using the derived category?

You might want to try tilting modules. Those at least provide a generating set with trivial self-extensions.