got / gotten
The past forms of get, and have got for possession.
Got is the past tense of get: She got the key. Gotten is the past participle: She has gotten the key. In British English, got is the past participle, so She has got the key is standard British usage.
In American English, got is the wrong past participle, so have got can only be a casualism, not correct standard English. In place of have got, simply use have: I have the key. It means exactly the same thing.
Examples
UseShe got the file this morning. (past tense of get)
UseShe has gotten the file. (obtained the file)
UseShe has the file. (possesses the file)
AvoidShe has got the file. (unless the speaker is being casual)