Where does local variables actually allocated within CLR?

I'm just going inside the CLR and IL and I'm confused by this thing.

I have the following C# code:

int x = 1;
object obj = x;
int y = (int)obj;

And IL disassemble for this

      // Code size       18 (0x12)
  .maxstack  1
  .locals init ([0] int32 x,
           [1] object obj,
           [2] int32 y)
  IL_0000:  nop
  IL_0001:  ldc.i4.1
  IL_0002:  stloc.0
  IL_0003:  ldloc.0
  IL_0004:  box        [mscorlib]System.Int32
  IL_0009:  stloc.1
  IL_000a:  ldloc.1
  IL_000b:  unbox.any  [mscorlib]System.Int32
  IL_0010:  stloc.2
  IL_0011:  ret

So, the ldloc.0 instruction "Loads the local variable at index 0 onto stack.". But where does the locals really stored and where does they loaded from. Because I thought that there are two places where the memory can be allocated: thread stack and heap. And variables should be stored in the stack.

Now, I suppose, that the stack is just an "evaluation stack", while the memory allocation for variables is an implementation detail and depend on platform and JIT compiler. And we actually can split the memory used by our programm on evaluation stack, managed heap, and locals allocated memory.

Is this true? Or there are some other mechanism here?