MathOverflow is a question and answer site for professional mathematicians. Join them; it only takes a minute:

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

Suppose I have a smooth projective variety $X$, and a semi-orthogonal decomposition of its bounded derived category:

$$D^b(X)= < A, E_1, E_2, ... , E_n >$$

where the $E_i$ are fully faithful, saturated (and hence admissible) subcats of $D^b(X)$. Is A authomatically saturated/admissible? Why? If not, under what assuptions?

share|cite|improve this question
up vote 1 down vote accepted

Yes, it is. See Bondal, A. I.; Kapranov, M. M. Representable functors, Serre functors, and reconstructions.

share|cite|improve this answer

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.