Given a group scheme $X$ over $S$, where $S$ is an arbitrary locally noetherian scheme, then how does one define the Lie algebra of $X$? And how does it behave with respect to base change?
Is there any good reference for the theory of group schemes apart from Demazure/Gabriel's book about Algebraic Groups?
All of the treatings I have encountered only care about affine schemes, often over a base field. Where can I find a more general exposition?