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1 results

  • Function Spaces and Continuous Algebraic Pairings for Varieties

  • Eric M. Friedlander, Mark E. Walker
  • Journal:
    Compositio Mathematica / Volume 125 / Issue 1 / January 2001
    Published online by Cambridge University Press:
    04 December 2007, pp. 69-110
    Print publication:
    January 2001
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  • Given a quasi-projective complex variety X and a projective variety Y, one may endow the set of morphisms, Mor(X, Y), from X to Y with the natural structure of a topological space. We introduce a convenient technique (namely, the notion of a functor on the category of ‘smooth curves’) for studying these function complexes and for forming continuous pairings of such. Building on this technique, we establish several results, including (1) the existence of cap and join product pairings in topological cycle theory; (2) the agreement of cup product and intersection product for topological cycle theory; (3) the agreement of the motivic cohomology cup product with morphic cohomology cup product; and (4) the Whitney sum formula for the Chern classes in morphic cohomology of vector bundles.