Function spaces and continuous algebraic pairings for varieties (Q2709819)

Given a quasi-projective complex variety \(X\) and a projective variety \(Y\), one may endow the set of morphisms, \(\text{Mor}(X, Y)\), from \(X\) to \(Y\) with the natural structure of a topological space. In this paper a convenient technique (namely, the notion of a functor on the category of `smooth curves') is given for studying these function complexes and for forming continuous pairings of them. Building on this technique, the following results are established, includingNEWLINENEWLINE(1) the existence of cap and join product pairings in topological cycle theory;NEWLINENEWLINE(2) the agreement of cup product and intersection product for topological cycle theory;NEWLINENEWLINE(3) the agreement of the motivic cohomology cup product with morphic cohomology cup product; andNEWLINENEWLINE(4) the Whitney sum formula for the Chern classes in morphic cohomology of vector bundles.