First, remove their food source. If you feed wild birds, switch to a seed that pigeons hate, like safflower or nyjer. They’ll turn their beaks up at it.
Also, clean up fallen food immediately. Yes, it’s annoying. But imagine a pile of pizza crusts on your coffee table—pigeons feel the same way about spilled seed.
Cover your compost with a tight lid. Pigeons are basically flying raccoons. They’ll dig through anything.