Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. 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

I am reading about Serre duality theory in algebraic geometry from Hartshorne, and am wondering what kinds of applications it has. It seems that most applications go through some version of the Riemann-Roch theorem, which is then used to study algebraic curves and surfaces.

What are some other applications of Serre duality?

share|cite|improve this question

My favorite is the following. Serre duality shows that the derived category of a (smooth) algebraic variety has a Serre functor, which is not just an invariant of the derived category but it also produces left (right) adjoint to a functor which has right (left) adjoint.

share|cite|improve this answer
Serre functors are an extremely powerful tool in the study of derived categories of coherent sheaves, see for some references and more information. – Adeel Jul 29 '13 at 18:40

Your Answer


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

Not the answer you're looking for? Browse other questions tagged or ask your own question.