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We prove in this paper the smoothability of cycles modulo rationalequivalence in the Whitney range, that is, when the dimension is strictlysmaller than the codimension. We introduce and study the class of cyclesobtained as ``flat pushforwards of Chern classes" (or equivalently, flatpushforwards of products of divisors) and prove that they are smoothable in theWhitney range. Our main result is that all cycles (of any dimension) on asmooth projective variety are flat pushforwards of Chern classes. In the caseof abelian varieties, one can even restrict to smooth pushforwards of Chernclasses.

Flat pushforwards of Chern classes and the smoothability of cycles in the Whitney range