#### When is a map of topological spaces homotopy equivalent to an algebraic map?

My question is simple, but I don't expect there are any simple answers.

Let $$X$$ and $$Y$$ be a pair of schemes, and let $$X(\mathbb{C})$$ and $$Y(\mathbb{C})$$ denote their respective spaces complex points. Suppose we are given spaces $$X'\simeq X(\mathbb{C})$$ and $$Y'\simeq Y(\mathbb{C})$$, where $$\simeq$$ denotes weak equivalence of spaces.

What is known about necessary or sufficient conditions for a map $$f':X'\to Y'$$ to be homotopy equivalent to a map coming from a morphism $$f:X\to Y$$ of schemes?

I am specifically interested in showing that a particular map of spaces is not homotopy equivalent to a map coming from a morphism of schemes.