Microsoft has posted up some information pertaining to levels, versions, and revisions of Operations Manager that have support for Windows Server 2012. It’s a mixed bag, really, from no support, to partial support, to future support.
You can read the information in it’s entirety here: Windows Server 2012 – System Center Operations Manager Support, however, in brief, it’s like this:
|Operations Manager 2007 R2 Agent on WS2012||Not Supported|
|Operations Manager 2007 R2 Server on WS2012||Not Supported|
|Operations Manager 2012 Monitoring of WS2012||Supported|
|Operations Manager 2012 Server on WS2012||Not Supported|
|Operations Manager 2012 SP1||Full Support (agent, monitoring, server)|