There are a lot of discussions on the finiteness properties (FP_n types) of an arithmetic group over a function field. (e.g. http://www.math.utah.edu/~wortman/Frozen_Artihmetic_Finiteness.pdf, http://www.degruyter.com/view/j/crll.1998.1998.issue-495/crll.1998.023/crll.1998.023.xml).
My question is: are there similar discussions on the general linear group(or more general group schemes) over polynomial algebra(integer or finite field coefficients) in multi variables?
Thanks for any reply in advance.