Journal of the Mathematical Society of Japan

Moduli of stable objects in a triangulated category

Michi-aki INABA

Full-text: Open access


We introduce the concept of strict ample sequence in a fibered triangulated category and define the stability of the objects in a triangulated category. Then we construct the moduli space of (semi) stable objects by GIT construction.

Article information

J. Math. Soc. Japan, Volume 62, Number 2 (2010), 395-429.

First available in Project Euclid: 7 May 2010

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 14D20: Algebraic moduli problems, moduli of vector bundles {For analytic moduli problems, see 32G13} 18E30: Derived categories, triangulated categories

moduli triangulated category


INABA, Michi-aki. Moduli of stable objects in a triangulated category. J. Math. Soc. Japan 62 (2010), no. 2, 395--429. doi:10.2969/jmsj/06220395.

Export citation


  • T. Bridgeland, Stability conditions on triangulated categories. Ann. Math. (2), 166 (2007), 317–345.
  • A. Bondal and D. Orlov, Reconstruction of a variety from the derived category and the groups of autoequivalences, Comp. Math. 125 (2001), 327–344.
  • D. Huybrechts and M. Lehn, The geometry of moduli spaces of sheaves, Aspects of Mathematics, E31, Friedr. Vieweg & Sohn, Braunschweig, 1997.
  • M. Inaba, Toward a definition of moduli of complexes of coherent sheaves on a projective scheme, J. Math. Kyoto Univ., 42 (2002), 317–329.
  • A. D. King, Moduli of representations of finite-dimensional algebras, Quart. J. Math. Oxford Ser. (2), 45 (1994), no.,180, 515–530.
  • A. Langer, Semistable sheaves in positive characteristic, Ann. of Math. (2), 159 (2004), 251–276.
  • M. Lieblich, Moduli of complexes on a proper morphism, J. Algebraic. Geom., 15 (2006), 175–206.
  • M. Maruyama, Construction of moduli spaces of stable sheaves via Simpson's idea, Moduli of vector bundles (Sanda, 1994; Kyoto, 1994), 147–187, Lecture Notes in Pure and Appl. Math., 179, Dekker, New York, 1996.
  • C. S. Seshadri, Geometric reductivity over arbitrary base, Adv. in Math., 26 (1977), 225–274.
  • K. Yoshioka, Moduli spaces of twisted sheaves on a projective variety, Moduli spaces and arithmetic geometry, 1–30, Adv. Stud. Pure Math., 45, Math. Soc. Japan, Tokyo, 2006.
  • K. Yoshioka, Stability and the Fourier-Mukai transform I, Math. Z., 245 (2003), 657–665.