Wouldn't bring the carrier into the area bring it into range of Russian land and sea based anti ship weaponry? Why do that, it's a very big floating target at that point then?
It's not like there aren't a lot of ally air bases that the US couldn't use in the area.
According to RT, the Russians have treaties in place to have a lot of troops in the Crimea. Lots of other interesting tidbits about existing Russian-Ukrainian military treaties, though I don't think the treaties were written with these troops taking control of Ukrainian facilities in mind. Interesting thing is Russia still claims not to have deployed any troops.
http://rt.com/news/russian-troops-cr...medium=twitter