Identifier

etd-11152010-145059

Degree

Doctor of Philosophy (PhD)

Department

Mathematics

Document Type

Dissertation

Abstract

In this work we prove that the hermitian K-theory is geometrically representable in the A^1 -homotopy category of smooth schemes over a field. We also study in detail a realization functor from the A^1 -homotopy category of smooth schemes over the field R of real numbers to the category of topological spaces. This functor is determined by taking the real points of a smooth R-scheme. There is another realization functor induced by taking the complex points with a similar description although we have not discussed this other functor in this dissertation. Using these realization functors we have concluded in brief the relation of hermitian K-theory of a smooth scheme over the real numbers with the topological K-theory of the associated topological space of the real and the complex points of that scheme: The realization of hermitian K-theory induced taking the complex points is the topological K-theory of real vector bundles of the topological space of complex points, whereas the realization induced by taking the real points is a product of two copies of the topological K-theory of real vector bundles of the topological space of real points.

Date

2010

Document Availability at the Time of Submission

Release the entire work immediately for access worldwide.

Committee Chair

Schlichting, Marco

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