Motivic Homotopy Theory

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DMS-0403367Vladimir VoevodskyThe resources provided by this grant will be used primarily for research in the motivic homotopy theory. The motivic homotopy theory is a field of mathematics centered on a new way of using geometric intuition to deal with algebraic problems. It originated about ten years ago and became recognized after being used to prove the Milnor conjecture relating Galois cohomology, Milnor's K-theory and quadratic forms.Translating the intuition of the motivic homotopy theory into rigorous mathematical results requires sophisticated formalism, which, as of today, is only partly developed. During the time period covered by this grant the principal investigator plans to work on the parts of this formalism known as is the theory of cohomological operations in the motivic cohomology and the motivic Spanier-Whitehead duality.