Frobenius Green functors

Andy Baker (U Glasgow)

Wednesday 18th January, 2012 16:00-17:00 204

Abstract

Green functors are contravariant functors on the category of finite groups which take values in algebras over some commutative ring equipped with certain covariant maps satisfying Frobenius reciprocity and Mackey formulae. I will discuss such functors where the algebras are finite dimensional and local over a field of positive characteristic $p$. In particular, requiring that the values are Frobenius algebras leads to an interesting theory. To get more concrete examples it seems necessary to impose more structure: I will consider the situation where the tower associated to cyclic groups of orders which are powers of $p$ gives rise to a $p$-divisible group scheme, associated with a sequence of bicommutative finite Hopf algebras. The motivation for this comes from trying to understand the Green functors associated to Morava $K$-theories of classifying spaces of finite groups.

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