Mathematical Sciences: K-Theory of Fields

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This project is concerned with the K-theory of fields. The principal investigator will attempt to extend the results of Rost and Merkerjev-Suslin. He will employ the techniques of relative K-theory to provide an understanding of the weight three K-theory of fields. He will also employ his recently constructed relative Milnor K-groups to construct motivic complexes. This research is concerned with algebraic K-theory. In a broad sense algebraic K-theory concerns the evolution of concepts from linear algebra such as basis and vector space. This work has significant implications for number theory and algebraic geometry, and promises to make exciting connections between a number of different areas in mathematics.