Abstract: The local-global conjectures have been a central area of research in local representation theory since the 1970s and in recent years considerable progress has been made on them. That being said none has yet been proved in complete generality. One area of work has been in finding equivalent statements to these conjectures. 

I will define what I mean for a function on groups to be chain local and then extend this idea to functions on blocks of groups. I will then go on to discuss how this definition can be used to rephrase the Alperin-McKay conjecture in terms of a function on blocks being chain local.