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

8815084 托马森 埃里森将在稳定同伦中发展新的方法 通过引入代数几何的思想来建立理论。 之间 其他事情，这应该澄清的特权作用， 稳定同伦范畴，给新的洞察关系 在稳定和不稳定同伦之间，并产生一个新的 包含了Spanier-Whitehead Serre-Grothendieck对偶 埃里森还将在他以前的工作基础上， 局部化的代数K-理论的计划，在这个新的 上下文，攻击本地化的K理论 非交换环和Waldhausen空间的K-理论。

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.