Let A —> B be a ring map. Assume
- A ⊂ B is an extension of domains,
- A is Noetherian,
- A —> B is of finite type, and
- the extension f.f.(A) ⊂ f.f.(B) is finite.
Let p ⊂ A be a prime such that dim(Ap) = 1. Then there are at most finitely many primes of B lying over p. See Tag 02MA.