Motivic Homotopy Theory

DMS-0403367弗拉基米尔Voevodsky该补助金提供的资源将主要用于研究动机同伦理论。动机同伦理论（motivic homotopy theory）是一个数学领域，其核心是使用几何直观来处理代数问题的新方法。它起源于大约十年前，并在被用来证明与伽罗瓦上同调、米尔诺尔K理论和二次型相关的米尔诺尔猜想后得到认可。将动机同伦理论的直觉转化为严格的数学结果需要复杂的形式主义，截至今天，这只是部分发展。 在这段时间内所涵盖的补助金的主要研究人员计划工作的一部分，这种形式主义被称为是理论的cohomological业务在motivic上同调和motivic西班牙人，怀特黑德二元性。

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.