2
$\begingroup$

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?

$\endgroup$

1 Answer 1

1
$\begingroup$

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

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

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