We show boundedness for PT-semistable objects of any Chern classes on a smooth projective three-fold X. Then we show that the stack of objects in the heart Coh≥1(X),Coh≤2(X) satisfies a version of the valuative criterion for completeness. In the remainder of the paper, we give a series of results on how to compute cohomology with respect to this heart. © 2011 Elsevier Inc.
Lo, J. (2011). Moduli of PT-semistable objects I. Journal of Algebra, 339(1), 203–222. https://doi.org/10.1016/j.jalgebra.2011.04.035