Georg Tamme (Regensburg): On the K-theory of pullbacks. (Oberseminar Topologie)
Montag, 10.12.2018 14:00 im Raum N3
In this talk I will discuss recent joint work with Markus Land.
To any pullback square of ring spectra we associate a new square of ring spectra, which agrees with the old square in three corners. Only the lower right corner is replaced by a new ring spectrum whose underlying spectrum is a derived tensor product of the other three corners. The new square has the property that it induces a pullback square upon applying K-theory, or in fact any other `localizing invariant? to it. From this we easily deduce a number consequences. For example, we obtain simple proofs for excision in periodic cyclic homology in characteristic 0 (originally due to Cuntz and Quillen), excision for the fibre of the cyclotomic trace map (originally due to Cortinas, Geisser-Hesselholt, and Dundas-Kittang), results about torsion in relative and birelative K-groups (generalizing results of Geisser-Hesselholt), and conditions for excision in algebraic K-theory (refining results of Suslin-Wodzicki).
In the talk I will explain the main result and illustrate its use in some applications and examples.