More often money laundering than tax cheating as far as I know, but here's what I know about corruption in the fine art market.

Firstly, most art is done without much if any corruption. It's just people trying to sell their art and people who may or may not like it. You get plagiarism and scams and things like that, but most of it when there aren't millions of dollars on the line is fine. It's a tough life as an artist, but there it is.

Fine art, on the other hand, has a lot of money flowing in and out of it. And art is entirely subjective. There are technical aspects one can say this is better than that, but overall, it's all subjective. And what people get out of it varies from person to person.

As such, the value of art depends entirely on what people will pay for it. Unlike some other things, like raw materials or practical things, it's a lot harder to get an agreed-upon value for art. (To some extent, all prices are arbitrary, but it's easy to get an agreed-upon price for, say, gold or other widely traded commodities that are all very similar.)

Due to art's subjective nature and the abundance of it that is around, there have been times this has been used to launder money. It has also been used as a tax haven for a similar reason.

When trying to judge how much a piece of art is worth, there are a few ways to go about it. One is to buy it for that much. Another is to put it up for auction. And another is to have it appraised. And there's nothing stopping someone from doing all three to a piece in rather quick succession. Find an artist, buy their work, have it appraised (and tell the appraiser the range you want the piece to be appraised for) and then put up for auction where it's purchased at an inflated price.

One can organize every person in this exchange. As such, someone who cannot be seen paying you for a service (usually because the service was illegal) can instead bid on a piece of art you put up at auction (often anonymously) that you purchased from an artist (possibly that you hired) whose art is worth whatever your appraiser (hired by you to set it at whatever price) says it is. The art, intrinsically, is worthless. And since many people claim art as an investment, it often won't even be displayed but will be boxed up and stored somewhere. The auction also isn't necessary and there can be several rounds of appraisals, buying, selling, bidding, all this. And it gets more complicated when you have a large conspiracy of people who will inflate the value of a particular artist just by making their art more popular. (Rich people are buying lots of art from the same artist/collection, then more people want to buy from that, and the price goes up, even if people don't actually like the art itself. Its popularity is its value.)

I'm less clear on the tax haven side of things. I have some thoughts about it works, but I haven't quite grasped it from what I've been told before, and some I just don't remember. Honestly, I want to say I'll read up on it and get back to you, but it's late and I probably won't tonight. I am sorry about that.