Low volts

I have a 2002 Buick park avenue. Recently my car died. It
had low volts. When I went to pull over my abs light and my
security light came on. My low voltage light was on the
whole time. When I stopped the rpm went to 2,100 and
stayed. It would not go any lower. I shut the car off and
tried to restart it. When I did that it acted like a dead
battery. 30 minutes later it started right up. I was able to
drive it home. The next day it did the same thing. I think it
might be the alternator because when it is running and you
disconnect the battery it would die.