Speaker
Tobias Lenz
Abstract
Algebraic K-theory is an important invariant encoding at the same time arithmetic, topological, and geometric information. Recently, there has been a renewed interest in refinements of K-theory that take into account additional ‘symmetries’ of the input category, for example through the work of Merling, May, and others on G-equivariant algebraic K-theory (for a fixed finite group G) or through Schwede’s construction of global algebraic K-theory. While these two concepts are somewhat similar in spirit, they are ultimately quite different, and neither of them specializes to the other. In this talk I will introduce G-global algebraic K-theory as a synthesis of the above two approaches and go into some of the theory behind it. I will then explain how one can use this theory to generalize Thomason’s classical result that K-theory exhibits symmetric monoidal categories as a model of connective stable homotopy theory to G-equivariant, global, and G-global contexts.