References on derived categories:

• Articles:

  • Thomas, Derived Categories for the Working Mathematician. This is great for getting a feel of what derived categories are. Very non-intimidating at only 13 pages.

  • Caldararu, Derived Categories of Sheave: a Skimming. A clear introduction to derived categories in the context of algebraic geometry.

• Books:

• • Weibel, An Introduction to Homological Algebra. See Chapter 10 for a very quick introduction to the derived category.

• • Huybrechts, Fourier-Mukai Transforms in Algebraic Geometry. This gives a comprehensive introduction to triangulated categories in general, derived categories, Fourier-Mukai transforms, and some basic applications of these things.

  • Gelfand and Manin, Methods of Homological Algebra. This is a good reference for t-structures - see Chapter IV, Section 4.

General references on Bridgeland stability conditions:

• Bayer, A Tour to Stability Conditions on Derived Categories. An comprehensive introduction to Bridgeland stability conditions, that grew out of a summer course for graduate students.

• Bridgeland, Stability Conditions on Triangulated Categories. Where it all began!

Bridgeland stability conditions on curves:

• Okada, Stability Manifold of P1

• Macri, Stability Conditions on Curves

Bridgeland stability conditions on surfaces:

• Bridgeland, Stability Conditions on K3 Surfaces. The very first examples of stability conditions (on surfaces).

• Arcara and Bertram, Bridgeland-Stable Moduli Spaces for K-Trivial Surfaces. One of the first references on moduli spaces of Bridgeland-stable complexes. Section 2 of the paper is also a clear and concise summary of the basics on derived categories and stability conditions.

This is a very incomplete list - if there are other references that you think should go on the list, please let me know!

(Last updated in spring 2016.)