| Résume | The aim of this long-term project (which is joint with Jan Stovicek)
is to show that some aspects of classical representation theory are completely
formal and are valid in any abstract stable homotopy theory. More specifically,
while more classical studies focus on representations over a field, we obtain
similar results for representations over rings, in quasi-coherent modules on
schemes, in dg-modules over dgas, in module spectra over ring spectra, and
other stable homotopy theories.
In this talk I give an introduction to this project and recall some basics
concerning derivators, which are then illustrated by sketch-proving an abstract
tilting result for trees.
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