Algebraic Geometry of Triangulated Categories and the Foundations of Stable Homotopy Theory

8815084托马森将通过引入代数几何的思想，发展稳定同伦理论的新方法。其中，这应该澄清稳定同伦范畴的特权作用，为稳定同伦和不稳定同伦之间的关系提供新的见解，并产生一个新的包容对偶理论，包括西班牙-怀特黑德和Serre-Grothendieck对偶。托马森还将在这一新的背景下建立在他在方案的代数K-理论中的局部化工作的基础上，攻击非对易环的K-理论和Waldhausen空间的K-理论中的局部化。

8815084 Thomason Thomason will develop new methods in stable homotopy theory by introducing ideas from algebraic geometry. Among other things, this should clarify the privileged role of the stable homotopy category, give new insight into the relation between stable and unstable homotopy, and yield a new encompassing duality theory containing both Spanier-Whitehead and Serre-Grothendieck duality. Thomason will also build on his previous work in localization in the algebraic K-theory of schemes in this new context, to attack localization in the K-theory of non-commutative rings and in the Waldhausen K-theory of spaces.