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Well, if you just map the kernel directories in every process, then all you have to do is to keep directories up to date, and never touch to the PDE mapping the kernel (they'll be allocated statically).

Another option is to provide a Master Page Directory which is always up to date for the kernel and give it a "version number" (operations count). When you switch to another process, check it's own directory has the same version as the Master Page Directory. If not, update it

Tim Robinson wrote: If each process's page directory uses the kernel's page tables for the kernel region then the problem becomes less. That is, each process shares the same kernel page tables. Then most kernel allocations will apply automatically to all processes. It's only when you map a whole new page table that you need to update other processes, and you can do that whenever you see a page fault in the kernel region.

I would have to:
- temporary map the current page dir into the kernel space,
- switch to another task address space (still remaining into the kernel code),
- free the physical frame associated with the task's page dir,
- unmap the temporary mapped page dir.

killAddressSpace(<kernel mode>) {
    foreach pde in CurrentDirectory.list() {
       if (!pde.belongsKernel() && !pde.isPageDirectory())
          Pager.free_frame(pde.frame);
    }
    Scheduler.enterCritical();
    Pager.sendMessage(DELAYED_FREEFRAME, CurrentDirectory.frame);
    ProcessManager.sendMessage(DELAYED_KILLPROCESS,pid);
    Scheduler.dropTask();
}