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Derived Categories and Stability Conditions

I am writing some stuff in derived categories and stability conditions.

A tour to stability conditions on derived categories

I generally follow Arend Bayer's note with same title. I try to explain as much as possible. I sincerely thank Chunyi for his help in understanding this note. Feel free to contact me about these writings.

Stability in Abelian Categories

This is basically second section of Arend Bayer's lecture note. This includes classical stability conditions on curves, quiver representations, and exercises.

Derived Categories and T-Structures

This is the third section of Arend Byer's note. This include some definition of derived category and bounded t-structure, tilting and so on. Exercise and some points related to the standard t-structure are unsolved as I have not fully understood what it means for standard t-structure. I will update it later on. Note: this part has some errors and lack some solution to exercises. I already have ideas about them but do not have time to fix them. I will try to do them in two weeks. Feel free to contact me about these.

Stability Conditions on a Triangulated Category

This is fourth part of the same note. Basically we (well not we, but you know) define what is a Bridgeland stability condition on a triangulated category, and its equivalence to heart of a bounded t-structure with extra conditions. Trivial examples are given. Also a funny remark.

Space of Stability Conditions

This is the fifth part of the note. This gives the deformation theorem of Bridgeland, and gave proof and some examples of them.