Christian Dahlhausen  (Universität Heidelberg): Duality in (perfect) motivic homotopy theory

This talk treats a conjectured duality on modules over
K-theory in the stable homotopy category of a scheme whose dualising
object is given by G-theory. I shall explain a proof of the conjecture
for quasi-excellent schemes in characteristic zero. In order to approach
the conjecture in positive characteristic, I sketch the construction of
a “perfect motivic homotopy category” and compare it to the classical
homotopy category. For this perfect category, I shall sketch the proof
of an analogous version of the duality conjecture. This is joint work
with Denis-Charles Cisinski, Jeroen Hekking, and Storm Wolters.

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