General rarity:
* Scarcity: This is the most common and direct translation of "rare" as an abstract noun.
* Uniqueness: This emphasizes the special or one-of-a-kind quality of something rare.
* Exceptiveness: This emphasizes the rarity of something being outside the norm.
Rarity in specific contexts:
* Infrequency: This focuses on the low rate of occurrence of something.
* Seldomness: Similar to "infrequency", this emphasizes how rarely something happens.
* Elusive: This implies that something is difficult to find or obtain due to its rarity.
The best abstract noun for "rare" will depend on the specific meaning you want to convey.