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We provide partial results towards a conjectural generalization of a theoremof Lubotzky-Mozes-Raghunathan for arithmetic groups (over number fields orfunction fields) that implies, in low dimensions, both polynomial isoperimetricinequalities and finiteness properties. As a tool in our proof, we establishpolynomial isoperimetric inequalities and finiteness properties for certainsolvable groups that appear as subgroups of parabolic groups in semisimplegroups, thus generalizing a theorem of Bux. We also develop a precise versionof reduction theory for arithmetic groups whose proof is, for the most part,independent of whether the underlying global field is a number field or afunction field.

Filling boundaries of coarse manifolds in semisimple and solvable arithmetic groups