MathOverflow is a question and answer site for professional mathematicians. It's 100% free, no registration required.

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

Let $f : X\rightarrow Y$ be a morphism of scheme. For any point $y\in Y$, the fibre of $f$ over $y$ is defined to be $X_y = X\times_Y Spec(k(y))$. Then the underlying set of $X_y$ is bijective with $f^{-1}(y)$.

When $f$ is not surjective and $y\in Y-f(X)$ then the underlying set of $X_y$ has to be empty set. Then what is mean by empty scheme?

share|cite|improve this question
5  
The empty scheme is the spectrum of the zero ring. – jlk Dec 10 '10 at 5:05
1  
The empty ringed space is the empty topological space together with the (unique) zero sheaf. – Martin Brandenburg Dec 10 '10 at 7:56

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.