Correct. Not a virus, not a trojan. Adware-url.gen is pretty much what the name says it is, a by-product of an adware program.
This is a generic detection covering URL shortcut files created by various Adware programs. These files do not directly impact system performance, but may clutter a user's desktop, start menu, favorites, and other folders. Such URL shortcuts are meant to direct users to web pages that contain advertising content.
It's a generic name for a class of PUP so it won't tell you which adware program created it. If you want to prevent them from loading up in the first place you need to get an add-on for your browser to stop adware at source. There's a whole range of these, do a search in the Get Add-Ons section and pick one you like the look of.
Thanks very much for the detailed info Hayton...as always!