This should probably be in the Nano forum, but the particular question would be the same for a TX2 (other than perhaps a different kernel).
The “ARCH” names the architecture being built. “arm64” is 64-bit ARMv8-a, which is valid for both Nano and TX2. However, this is not the tool…when a cross compile occurs you must tell it what architecture to output for, and in this case it knows arm64. Then you must tell it which tool to use to produce that since it isn’t a native tool. This is where the original failure appears, and perhaps is for you too:
…doesn’t have anything after the “=”, and so it is empty. This would be a prefix path to the cross tool chain. Example: “CROSS_COMPILE=/usr/lib64/ccache/aarch64-linux-gnu-” (which happens to be on a Fedora host…Ubuntu would probably be a bit different).
When compiling on command line there are certain arguments a kernel compile will look for in the environment. If you explicitly give those arguments in the compile line, then that takes precedence. If neither the command line nor environment has those, then the compiler considers that no such option was requested. A kernel build with “ARCH=arm64” is the same as if prior to the command you had instead set an environment variable via “export ARCH=arm64” (the “export” says to “remember” this). The same is true of the location of cross compile tools…you could name a prefix to tools via “CROSS_COMPILE=/some/where”, or instead by using “export CROSS_COMPILE=/some/where” prior to the command.
Most kernel builds will pick up on the “export” even if the build is from a third party script, but not all. It just depends.
Incidentally, you can skip all of the cross tools and cross compile and build natively on a Jetson. The TX2 makes this easy, and probably the Nano as well, but the Nano will have less RAM and run slower (cross compile would definitely be faster, but also more complicated). As soon as you build on the native architecture life is much simplified.
FYI, I suggest sticking to a single thread in the forum. Too many threads makes it hard to answer. In the case of cross compile though it tends to be common ground on several Jetsons, and more specifically becomes a question of the host PC setup (it isn’t completely wrong to ask here).