Hi everyone,
This is more of a tip based on my experience with the above codes.
I have a 09 Aveo sedan I bought used. Car threw P2135 code and went into limp mode which I ‘fixed’ by shutting it down then starting 5 min later. Happened again, then again, in more frequent intervals. It got so bad that the car went into limp mode as soon as I started it. Car also started throwing P2101 along with 2135. When it did work, I noticed the car was very hesitant to upshift when accelerating (rpm would fluctuate rapidly, especially going uphill). What completely fixed the issue for me was a connector on the air duct coming out of the intake box was loose, and had a lot of dust inside. After cleaning it and re-connecting it, car ran smoothly, no more hesitation in upshifting and the code hasn’t come back yet. I hope this helps somebody and saves some money and frustration.