Denis-Charles Cisinski

Invariance of K-theory under derived equivalences
Monday, July 27, 3:00--4:00, MIT Room 2-131

Abstract:

K-theory is invariant under derived equivalences
for Waldhausen categories with (non necessary functorial)
cylinders. This can be proved by a characterization of
of derived equivalences by an elementary approximation property.
This can even be pushed further by producing an equivalence between
the homotopy category of (suitable) Waldhausen categories (up to
derived equivalence) and the homotopy category of finitely cocomplete
infinity-categories with a zero object, and by proving that Waldhausen
K-theory is compatible with this equivalence. Note that similar
results have been obtained by Blumberg and Mandell through
slightly different methods.