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 [tag:congruences-and-remainders] as a synonym for [tag:modular-arithmetic];
* Create a [tag:congruence-relations] tag (appropriately referred to in the [tag:congruences-and-remainders]/[tag:modular-arithmetic] excerpt, to avoid mistagging);
* Create a [tag:geometric-congruence] or [tag: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 [tag:congruences].