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

8815084 Thomason Thomason将引入代数几何的思想，发展稳定同伦理论的新方法。除其他外，这将澄清稳定同伦范畴的特权作用，对稳定同伦与不稳定同伦之间的关系提供新的见解，并产生一个包含西班牙-怀特海和Serre-Grothendieck对偶的新的包罗性对偶理论。Thomason还将在他之前在代数k -理论的局部化方面的工作的基础上，在这个新的背景下，攻击非交换环的k -理论和空间的Waldhausen 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.