I'm looking to learn about integral structures (or models?) on classical algebraic groups.


To begin with I have been learning about algebraic groups, quadratic forms and lattices. And also looking at this paper by Jonathan Hanke called "Algorithms for computing maximal lattices in bilinear (and quadratic) spaces over number fields" available here <http://arxiv.org/pdf/1208.2481.pdf> 


The thing is I want to learn about these integral structures but can't seem to find a good place to learn about them.


Thanks



What should I read if I want to learn about integral structures on classical algebraic groups?
not sure what you mean by good. The standard books on quadratic forms over number fields are in Hanke's references. I would add that Hanke studied under Shimura, so you should take a look at [shimura\_2010](http://www.springer.com/mathematics/algebra/book/978-1-4419-1731-7) and [shimura\_2012](http://www.springer.com/mathematics/computational+science+&+engineering/book/978-1-4614-2124-5), as the standard interplay is quadratic forms and modular forms. Note that the book that defined notation for a generation is O'Meara, in Hanke's references. I'm not sure Hanke mentions [Kitaoka](http://www.cambridge.org/us/academic/subjects/mathematics/number-theory/arithmetic-quadratic-forms?format=PB). 


For other classical groups, [Grove](http://www.ams.org/bookstore-getitem/item=GSM-39) is unusual in including characteristic 2 in full detail.


Finally, i never got interested in using number fields. So i like [Cassels, Rational Quadratic Forms.](http://store.doverpublications.com/0486466701.html) 


Added in proof: take a look at [THIS](http://zakuski.math.utsa.edu/~kap/forms.html) and [THIS](http://www.math.rwth-aachen.de/~Gabriele.Nebe/LATTICES/), maybe you will like something. 


