How Important is the rank of a school in a certain specialty?
Don’t trust the US News grad school subfield rankings at all.  They’re based entirely on surveys and most people don’t actually know a lot about things outside their speciality and their university.  So you infamously end up with high ranking places that actually don’t have anyone in the subfield.

If you want to know how good a school is in a subfield you’ll have to look into it seriously yourself.  Ask people you know in that subfield, look up the research interests in the department, find out whether their have been grad students their recently, after you get accepted visit the dept and ask questions.

That said, I think in the US in math it’s a mistake to narrow down to a specialty before you go to grad school.  You have a year of grad school before you have to pick an advisor, and you’ll learn a lot in that year.  Plus you’re more likely to find a good advisor match if you are picking between 20 potential advisors and not 2.