On the K-theory of pullbacks
Location: MSRI: Simons Auditorium
I will report on joint work with Markus Land. To any pullback diagram of ring spectra we associate a new square of ring spectra which becomes cartesian upon applying K-theory, or in fact any localizing invariant. The new square canonically maps to the original one, and this map is an equivalence in three corners. In the fourth corner, this map is generally not an equivalence. However, we understand this map well enough to deduce simple proofs of various excision results, most of which were previously proven by different methods in work of Suslin-Wodzicki, Cuntz-Quillen, Cortiñas, and Geisser-Hesselholt.