Picard Groups for Derived Module Categories

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Derived Categories (2016, methodology): “Zimmermann [132] (who had used the notation TrPic(A) for this group) and Yekutieli [165].”
Handbook of Tilting Theory: Fourier-Mukai transforms (2004, background): “ymplectic Dehn twist of Z associated to i. By the homological mirror symmetry conjecture there should be an analogous notion for derived categories of varieties. This was worked out in [73] (see also [41, 68]). It turns out that the analogue of a Lagrangian sphere is a so-called spherical object. To”
Braid cobordisms, triangulated categories, and flag varieties (2006, background): “• Actions generated by a chain of spherical objects [KS, ST, RZ , HK].”
A functor-valued invariant of tangles (2001, unknown): “III A simpler example of braid group actions was found in [ 52 ] and [39] and later considered in [53] and [27].”
On triangulated orbit categories (2005, result): “v-Seidel in [36]. Here the authors show that Db(B) admits a canonical action by the braid group on n + 1 strings, a result which was obtained independently in a similar context by Zimmermann-Rouquier [52]. The canonical generators of the braid group act by triangle functors Ti endowed with morphisms”
Picard Groups, Grothendieck Rings, and Burnside Rings of Categories (2001, methodology): “The latter have been introduced and studied by Miyachi and Yekutieli [35, 45] and by Rouquier and Zimmermann [41], as a follow-up to Rickard’s work on tilting complexes [39, 40].”