A version of continous cohomology for certain Hopf algebroids

Andy Baker (U Glasgow)

Wednesday 13th October, 2010 16:00-17:00 204


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. In Algebraic Topology this kind of example appears in connection with Lubin-Tate theory and Morava stabilizer groups.

Add to your calendar

Download event information as iCalendar file (only this event)