Skarner needs lots of mama/mana regen. This is fortunate, because when building him AP, it already makes most of your choices for you. You build Tear of the Goddess with Catalyst the Protector as your first two items in order to really maximize his mana as early as possible. This leads to a very high level of sustainability for Skarner, especially due to the massive heals he gives himself. I give him Boots of Swiftness instead of Mobility because the focus on AP Skarner isn't in Ganking, as it is with Jungle Skarner, but with utilizing Impale to the best of your abilities, and the extra speed of Boots of Swiftness means you'll pull your target that much further. For the mid-game, you upgrade the Tear into an Archangel's first, then quickly get yourself a Rod of Ages with that Catalyst. Once you have these, Skarner will snowball on his own, as well as Heal every time he levels, so that you can stay in-lane to perhaps fully purchase a Stinger or Nashor's Tooth the next time you have to go back to shop. This provides the Attack Speed necessary for Skarner to have most of his abilities off cooldown whenever he needs them. For his late game, Lich Bane makes his attacks between skills terrifying, and Rabbadon's Deathcap rounds out the build, pushing his AP high enough that Impale will do over 500 damage initially, and another 500 upon releasing the champ, allowing Skarner to kill squishies like Caitlyn or Vayne almost with a single spell, not to mention the insane distance you can cover using this build.