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?



Lie Algebra of Group Scheme
To elaborate on a comment by ulrich: SGA3 Exp. 2, section 4 treats Lie algebras of arbitrary group-valued functors over an arbitrary scheme (no locally noetherian hypothesis). I'm not sure what results you want with respect to base change, but most will follow straightforwardly from some combination of Definition 1.1 and Proposition 3.4.


