There is a textbook theorem that the categories of unipotent algebraic groups and nilpotent finite-dimensional Lie algebras are equivalent in characteristic zero. Indeed, the exponential map is an algebraic isomorphism in this case and the group structure can be defined in terms of the Lie algebra structure and vice versa via the Campbell-Hausdorff series, which is finite due to nilpotency. 


My problem is that I am unable to locate any textbook where this textbook theorem is stated. The books by [Borel](http://books.google.com/books?id=R31Z75Yvaj8C&printsec=frontcover&dq=Linear+algebraic+groups&cd=1#v=onepage&q=&f=false), [Humphreys](http://books.google.com/books?id=hNgRLxlwL8oC&printsec=frontcover&dq=Linear+algebraic+groups&cd=2#v=onepage&q=&f=false), [Springer](http://books.google.com/books?id=IVGvJ17FnMsC&printsec=frontcover&dq=Linear+algebraic+groups&cd=3#v=onepage&q=&f=false), [Serre](http://books.google.com/books?id=hasbV48Pm_AC&pg=PP1&dq=serre+lie+algebras+and+lie+groups&cd=1#v=onepage&q=&f=false) do not seem to mention this theorem.


The only reference I was able to locate is this [original paper](http://www.jstor.org/stable/2037665) by Hochschild (which refers to his earlier papers), but he does it in a heavy Hopf-algebra language that is good, too, but still leaves one desiring to find also a simple textbook-style exposition. Later Hochschild wrote a book "Basic Theory of Algebraic Groups and Lie Algebras" on the subject, to which I have presently no access, but judging by Parshall's [review](http://projecteuclid.org/euclid.bams/1183551302), it is certainly not textbook-style.


Could anyone suggest a simple reference for this textbook theorem?



References for theorem about unipotent algebraic groups in char=0?
Demazure-Gabriel, *Groupes algebriques*, Tome I (published in 1970) is a more explicit source, if available. Chapitre IV treats "groupes affines,
nilpotents, resolubles", while Chapitre V specializes to commutative affine groups.
Typically they work over an (almost) arbitrary field $k$, but IV.2.4 is
devoted to "groupes unipotents en caracteristique 0". This seems to be as
full an account as you will find in a textbook; see especially Corollaire
4.5 for the category equivalence you want. 


Later textbooks in English
including Hochschild focus mainly on the structure/classification of reductive
rather than arbitrary affine groups. Even this much of the story told without scheme language is fairly long for graduate courses. It's regrettable from the reference viewpoint that Demazure-Gabriel gave up after one volume. 


