Mac put to sleep, display wakes up for no reason

Apple keeps changing things and this may not be easy to solve.

1) Change and test the following Energy settings for a day or two.

If "Wake for network access" is On, turn it Off to eliminate that as a problem.

2) Think back and try to remember if you added any new USB devices around that time.

Anything from a TM backup drive, a USB hub, a USB keyboard or mouse can wake the iMac.

The only way to test those, is to disconnect those devices one at a time and see if the iMac stays asleep.

3) Lastly check to see if there are any other major appliances on the same AC wall circuit as the iMac.

Some thing like a refrigerator that cycles automatically, could be causing enough of a power sag to wake the iMac.

Sleep issues can be caused by all sorts of different things.

System Settings, Network Activity, USB Activity, Unstable Main Power.

Set sleep and wake settings for your Mac - Apple Support

In order for us to provide more detailed help with sleep issues.

What year model is that iMac and what macOS version is it running...?

Identify your iMac model - Apple Support

You're welcome.

If the network setting doesn't fix, I would move on to testing the existing USB devices.

👍 Keep us updated on your progress.