The notion of order in the stable module category

Martin Langer (Universit├Ąt Bonn)

Monday 16th March, 2009 16:00-17:00 Mathematics Building, room 204

Abstract

Let k be a field of characteristic p, and let G be a finite group. In 1986, Carlson proved that if p is odd then for every class x of even degree in the (Tate) cohomology of G, x annihilates the cohomology of k/x. Here k/x denotes some choice of cone of multiplication by x on k. For p=2 this statement is not always true, so we can ask why the prime 2 is so special in this situation. We have a similar phenomenon in stable homotopy theory: multiplication by p on the mod-p Moore spectrum S/p vanishes if and only if p>=3. Motivated by the proof of his Rigidity Theorem, Schwede introduced a notion of "order" on triangulated categories which to a certain amount explains this phenomenon. I will carry over this notion to the stable module category and give a generalized version of Carlson's result in which the prime 2 is not special any longer.

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