GrothendieckNeeman duality and the Wirthmüller isomorphism
Beren Sanders
What 


When 
Jun 10, 2016 from 12:15 pm to 01:15 pm 
Where  Bonn, Raum 1.008, MathematikZentrum, Endenicher Allee 60 
Contact Name  sachinidis 
Add event to calendar 
vCal iCal 
(Joint work with Paul Balmer and Ivo Dell'Ambrogio.) In this talk, I will discuss an intimate relationship between Grothendieck duality in algebraic geometry and the Wirthmüller isomorphism in equivariant stable homotopy theory. To this end, we will make a general study of the existence and properties of adjoints of an arbitrary coproductpreserving tensortriangulated functor between rigidlycompactly generated tensor triangulated categories. It turns out that the more adjoints exist, the more strongly related they must be to each other, and the result is a surprising trichotomy: There exist either exactly three adjoints, exactly five or infinitely many. Moreover, this analysis will provide us with purely formal, canonical constructions of Wirthmüller isomorphisms (when they exist) and demonstrate that Grothendieck duality is in fact a necessary condition for the existence of such an isomorphism. If time permits, I will mention some more recent developments which show that the Adams isomorphism can also be constructed in this way as a (suitably generalized) Wirthmüller isomorphism.