A version of continous cohomology for certain Hopf algebroids
Andy Baker (U Glasgow)
Wednesday 13th October, 2010 16:00-17:00 204
Abstract
In Galois cohomology, the commonly encountered situation has a profinite group
G (in practise a Galois group) acting discretely on an abelian group M (this
means that stabilizers of elements of M contain finite index subgroups).
There is a well known notion of continuous cohomology in this situation which
is widely used in Class Field Theory for example; it is built from a colimit
of cohomology of finite quotients of G.
I will discuss ways of extending this to commutative Hopf
algebras over commutative rings which are suitably topologised.,
then I will generalize this to suitably topologised commutative
Hopf algebroids.
A key example to bear in mind is that of a profinite group G
acting on a complete local ring (R,m)
so that m is preserved by G and each quotient R/m^k is acted on
discretely. The Hopf algebroid here is the dual object to the
twisted group ring R
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