WebJun 17, 2016 · For example, the derived category of quasi-coherent sheaves (or its various variants) is the category of coefficients for coherent cohomology, just as the derived category of ℓ -adic sheaves is the category of coefficients for ℓ -adic cohomology, or motivic complexes are the coefficients for motivic cohomology. WebIn my past research, I studied autoequivalence groups of the derived category (in [1,2,3,4]) and stability conditions in the sense of Bridgeland (in [5,6,7]). Recently, I am studying …
Category Theory in Context - Mathematics
WebSep 7, 2011 · In the case of derived categories, this requires also the tensor structure. We start with the classical case of the category of coherent sheaves (after Gabriel). We present afterwards a similar approach in the triangulated case, where serious difficulties arise. Finally, we explain how to deduce that a smooth projective variety with ample or ... WebA TOUR TO STABILITY CONDITIONS ON DERIVED CATEGORIES AREND BAYER ABSTRACT.These lecture notes are an introduction to the space of Bridgeland ... 5The K-group of an abelian category is the quotient of the free abelian group generated by its objects by the relation [B] = [A] + [C] for any short exact sequence A,!B C. canadian bachelor party
NOTES ON DERIVED CATEGORIES AND DERIVED FUNCTORS
WebIn general, given a generator of the derived category (or any triangulated category or stable infinity-category I suppose), the (generalized) theory of derived Morita … WebThe derived category of is the triangulated category We denote the unique functor whose composition with the quotient functor gives back the functor defined above. Using Lemma 13.6.4 we introduce the strictly full saturated triangulated subcategories whose sets of objects are The category is called the bounded derived category of . WebGiven A an abelian category, we denote by D.A/the derived category of A and we denote by Da.A/the full subcategory of objects with cohomology vanishing in degrees >a. Let Abe a differential graded (=dg) algebra. We denote by D.A/the derived category of dg A-modules and by A-perf the category of perfect complexes, i.e.,the canadian backbreaker rack