منابع مشابه
Algebraic K-Theory Eventually Surjects onto Topological K-Theory
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 algebrai...
متن کاملTopological K-theory of Algebraic K-theory Spectra
One of the central problems of algebraic K-theory is to compute the K-groups KX of a scheme X. Since these groups are, by definition, the homotopy groups of a spectrum KX, it makes sense to analyze the homotopy-type of the spectrum, rather than just the disembodied homotopy groups. In addition to facilitating the computation of the K-groups themselves, knowledge of the spectrum KX can be applie...
متن کاملA Descent Theorem in Topological K-Theory
4. Strategy of the proof. The first step is to remark the following basic fact : if Y is the product X x X with the action of G switching the factors, Y may be identified with the space of maps from EG to X, a space which is homotopically equivalent to X, since EG is contractible. 1This theorem is well known if A is the Banach algebra of real numbers : cf. [2], lemma 3.5 for instance. Other pro...
متن کاملSemi-topological K-theory Using Function Complexes
Abstract. The semi-topological K-theory K ∗ (X) of a quasi-projective complex algebraic variety X is based on the notion of algebraic vector bundles modulo algebraic equivalence. This theory is given as the homotopy groups of an infinite loop space K(X) which is equipped with maps K(X) → K(X), K(X) → Ktop(Xan) whose composition is the natural map from the algebraic K-theory of X to the topologi...
متن کاملTopological K-theory of Complex Projective Spaces
We compute the K-theory of complex projective spaces. There are three major ingredients: the exact sequence of K-groups, the theory of Chern character and the Bott Periodicity Theorem.
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ژورنال
عنوان ژورنال: Rocky Mountain Journal of Mathematics
سال: 2014
ISSN: 0035-7596
DOI: 10.1216/rmj-2014-44-1-235