diff --git a/arch/x86_64/pmap.c b/arch/x86_64/pmap.c
index 4af4390..6f2586b 100644
--- a/arch/x86_64/pmap.c
+++ b/arch/x86_64/pmap.c
@@ -1,4 +1,4 @@
-#include "socks/types.h"
+#include <socks/types.h>
 #include <socks/memblock.h>
 #include <socks/vm.h>
 #include <socks/printk.h>
@@ -33,10 +33,9 @@ static size_t ps_size(page_size_t ps)
 	}
 }
 
-static pmap_t alloc_pmap(pml4t_t **pt)
+static pmap_t alloc_pmap()
 {
 	pml4t_t *p = kzalloc(sizeof *p, 0);
-	*pt = p;
 	return vm_virt_to_phys(p);
 }
 
@@ -176,7 +175,7 @@ static kern_status_t do_pmap_add(pmap_t pmap, void *p, pfn_t pfn, vm_prot_t prot
 	/* if we're mapping a 1GiB page, we stop here */
 	if (size == PS_1G) {
 		if (pdpt->p_entries[pdpt_index] != 0) {
-			/* this slot points to a ptab, delete it.
+			/* this slot points to a pdir, delete it.
 			   if this slot points to a hugepage, this does nothing */
 			delete_pdir(pdpt->p_entries[pdpt_index]);
 		}
@@ -197,7 +196,7 @@ static kern_status_t do_pmap_add(pmap_t pmap, void *p, pfn_t pfn, vm_prot_t prot
 		pdir = vm_phys_to_virt(ENTRY_TO_PTR(pdpt->p_entries[pdpt_index]));
 	}
 
-	/* if we're ampping a 2MiB page, we stop here */
+	/* if we're mapping a 2MiB page, we stop here */
 	if (size == PS_2M) {
 		if (pdir->p_entries[pd_index] != 0) {
 			/* this slot points to a ptab, delete it.
@@ -234,13 +233,11 @@ void pmap_bootstrap(void)
 	}
 	size_t hugepage_sz = ps_size(hugepage);
 
-	pml4t_t *kernel_pml4t;
-	kernel_pmap = alloc_pmap(&kernel_pml4t);
+	kernel_pmap = alloc_pmap();
 
-	//do_pmap_add(kernel_pmap, NULL, 0, VM_PROT_READ, PS_2M);
-
-	/* map 2GiB at the end of the address space to cover
-	   the kernel and memblock-allocated data */
+	/* map 2GiB at the end of the address space to
+	   replace the mapping created by start_32 and allow access to
+	   the kernel and memblock-allocated data. */
 	uintptr_t vbase = VM_KERNEL_VOFFSET;
 	for (size_t i = 0; i < C_2GiB; i += hugepage_sz) {
 		do_pmap_add(kernel_pmap,