Functors of the Category of Abelian Sheaves on Regular Affine Scheme

In this short paper, we prove that if R is a regular local ring of unequal characteristic, then there exists an additive covariant functor G from the category of abelian sheaves on SpecR to the category of abelian groups such that idg(G(R)) >dimG(R). This result shows that the answer to the question 3.8 (ii) in [3] may be negative.