Why do the corners of my ABS object lift off the bed?
There are many different approaches to solving this issue and most of the answers already are spot-on. However, the fundamental reason for the "warping" is incorrect and inconsistent temperature across the material.

If there is too much fluctuation in the temperature across the object in this heated state can result in warping. The reason you see this mostly on the build plate is because the temperature of the first few layers of molten plastic vary much more against the build plate than against higher layers. Note that you can see additional warping mid-print using ABS and this can be a result of a draft or sudden drop in ambient temperature.

So, to help solve your problem, here are some suggestions (sorry if there are duplicates):


Completely enclose/seal your machine's build area to reduce (or eliminate if possible) draft and prevent the natural heat of the machine from escaping.
Increase the temperature on your build plate. I almost exclusively use ABS on my printer and I keep my HBP at about 112C. However, I live in the NW of the US, so my climate is naturally cooler than say Florida.
Alternatively, try decreasing the nozzle temperature to a lower point within the ABS melting range. This will just shorten the gap between the inconsistencies in temperature across layers. It is typically better to print at lower temperatures if you can help it. Obviously there are differences in the filament, so you'll have to find that "sweet spot".
Ensure your build plate is flat and your tape doesn't have bubbles. Your BP being flat should be a no brainer, but if your kapton tape (or whatever you use) has bubbles, your freshly printed plastic may not be getting the same temperature from the BP as the rest of your part. This is a bad thing as mentioned earlier.
Use extra adhesion techniques such as "ABS Glue" (ABS w/ acetone) or even hairspray. This works about 80% of the time for me, but can make it a bit difficult when removing the parts off the BP.