What is it based on? Happiness of provinces? Something else? thanks!

Quantity of provinces, the more provinces, the more corruption.

Maybe even Karma, but I'm not 100% sure.

Yeah karma affects corruption too.

There is this building called Dungeon which reduces it by like 10%. I've got it in the last shard, so haven't got the chance to use it yet. From the name I could guess it'll lower the karma/upset the population...

Also I think some provinces (or rather some races in provinces) affect corruption more than others, making it potentially very expensive to own that low-income orc or goblin province that in return increases your overall corruption...

Thanks but where can I see my karma?

It shows as your 'title'. So there is Dishonest, Evil, Just etc. Basically the worse naming gets the lower is the karma. Also at the finishing screen (maybe on highscore also) it is shown what title you currently possess.

Is it normal that your Karma title is behind your name without an article?
Sounds funny though.
In game I'm Cthulhu Pure.
Sounds more like a drink to me than an Astral lord but I digress...

It's normal, although probably just a blooper from the localization.

You'll also get your 'glory' title in front of your name in the campaign mode.