Running inside a Qemu virtual machine, I am trying to install Alpine
Linux onto a manually partitioned 4gb disk that contains only a single
ext4 root partition.  (No swap, no /boot.)

Syslinux loads, but prints the following error message:

SYSLINUX 6.04 EDD [snip]
Failed to load ldlinux.c32
Boot failed: please change disks and press a key to continue.

Does anyone have any idea what I might be doing wrong?

I boot alpine-extended-3.15.1-x86_64.iso in Qemu, and then run the
following commands:

#  apk  add  sfdisk
#  echo  2048  |  sfdisk  /dev/sda
#  sfdisk  --activate  /dev/sda  1
#  apk  add  e2fsprogs
#  mdev -s
#  mkfs.ext4  /dev/sda1
#  mount  -t ext4  /dev/sda1  /mnt
#  setup-alpine    # and select the defaults for everything
#  setup-disk /mnt
>>  Installing system on /dev/sda1
>>  extlinux: Not a directory: /mnt/boot
>>  100%
>>  => initramfs: creating /boot/initramfs-lts
>>  /boot is device /dev/sda1
>>  extlinux: no previous syslinux boot sector found
>>  You might need to fix the MBR to be able to boot

>>  Boot attempt #1:
>>    Booting from Hard Disk...

So I run the following:

#  cat  /usr/share/syslinux/mbr.bin  >  /dev/sda

>>  Boot attempt #2:
>>    Booting from Hard Disk...
>>    Missing operating system.
>>    Booting from Floppy...
>>    Boot failed: could not read the boot disk
>>    [snip]

So I run the following:

#  extlinux  --install  /mnt/boot
>>  /mnt/boot is device /dev/sda1

>>  Boot attempt #3:
>>    Booting from Hard Disk...
>>
>>    SYSLINUX 6.04 EDD [snip]
>>
>>    Failed to load ldlinux.c32
>>    Boot failed: please change disks and press a key to continue.

If I let setup-alpine partition the disk, then the boot will succeed.