  The paper studies lower bounds for the dimensions of projective
indecomposable modules for Chevalley groups G in defining characteristic p. The
main result extending earlier one by Malle and Weigel (2008) determines the
modules in question of dimension equal to the order of a Sylow p-subgroup of G.
We also substantially generalize a result by Ballard (1978) on lower bounds for
the dimensions of projective indecomposable modules and find lower bounds in
some cases where Ballard's bounds are vacuous.
