There seems to be considerable support for taking on this tag (+8/-0, which is "high", for questions about tagging).
This answer intends to poll the specific approach I suggested.
Concretely, I suggest to:
- Introduce congruences-and-remainders as a synonym for modular-arithmetic;
- Create a congruence-relations tag (appropriately referred to in the congruences-and-remainders/modular-arithmetic excerpt, to avoid mistagging);
- Create a geometric-congruence or geometric-congruences tag (I'm not knowledgeable in this area, so I hope someone else can provide a good tag wiki and excerpt -- and possibly a better tag name);
- Blacklist congruences.