Minnesota AG Keith Ellison filed docs this week asking Judge Cahill to impose a stiffer sentence come June than he otherwise might under state sentencing guidelines, which recommend just 12.5 years. Cahill doesn't have to play it by the book, though, and could give Chauvin the max of 40 years.

If he's going over 12.5 years ... Cahill would have to find evidence of aggravating factors in the case, and Ellison says there's more than enough of that.

While Ellison didn't say exactly what the state is seeking in terms of a sentence ... it sounds like they want Chauvin behind bars for way longer than just a decade and change -- arguing the guy was especially cruel while killing Floyd, as evidenced by the number of times he ignored Floyd's screams.

Ellison notes Chauvin stayed on Floyd's neck for over nine minutes, despite the fact George was telling cops how much pain he was in ... that he couldn't breathe ... and that he was going to die. Floyd complained about not being able to breathe a whopping 27 times.

Chauvin's defense attorney, Eric Nelson, is arguing for the opposite -- saying Chauvin was authorized to use that force for an actively resisting suspect. The problem with that argument is Chauvin's own superiors testified he'd broken department protocol.

Ellison's filing is interesting in light of what he said on "60 Minutes" last week -- that Chauvin shouldn't get the maximum sentence just to set an example. Instead, he said the judge should give him whatever the case merits.