I'm running precise, with kernel 3.2.0-53-generic. I'd like to upgrade it to 3.10, which according to Wikipedia, is the latest long-term stable release. From http://kernel.ubuntu.com/~kernel-ppa/mainline/, I see that Linux 3.10 is associated with Saucy. (v3.10.29) - is that a problem?
Also, is the process as simple as downloading the *.deb's and installing them? What are the potential problems?