Algebraic K-Theory Eventually Surjects onto Topological K-Theory
نویسنده
چکیده
Background. For X a smooth scheme over ~, K.t(X; 2g/{") is isomorphic to the usual rood(" topological K-theory of X as a complex manifold ([6]). In this case, Theorem 1 essentially answers a question of Fulton, [9], w 5. For many such X the mapp: Ko(X)~K~ot(X) cannot be a surjection, as non-trivial Hodge conditions on the Chern classes prevent some topological bundles from being stably algebraic. Nevertheless, Theorem 1 shows that the existence of these non-algebraic topological bundles is reflected in the higher-dimensional algebraic K-groups of X. There are several conjectures in this area which are part of the Lichten-
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