come under
verb
Definitions
To come underneath (something).
Example: Why don't you come under my umbrella? There's plenty of room.
To be included or classified under (a title, specified class etc.).
Example: To sympathisers, though, all of his crimes came under the general heading of misdemeanors.
To be subjected to, be under the auspices of.
Example: Eventually I was promoted, and a small team of recruits came under my authority.