Rickard, J.: Derived equivalences as derived functors, J. Lond. Math. Soc., II. Ser. 43(1), 37–48 (1991) MathSciNet Google Scholar Rouquier, R., Zimmermann, A.: Picard groups for derived module categories. Proc. Lond. Math. Soc., III. Ser. 87(3), 187–225 (2003) MathSci...
in this notes we start with the basic definitions of derived categories, derived functors, tilting complexes and stable equivalences of morita type. our aim is to show via several examples that this is the best framework to do homological algebra, we also exhibit their usefulness for getting new...
Stable functors of derived equivalences and Gorenstein projective modulesDerived equivalencestable functorGorenstein projective module16G1018E3018G25From certain triangle functors, called non-negative functors, between the bounded derived categories of abelian categories with enough projective objects, we ...
derivedfunctorscategoriesmulticomplexesmulticomplexhomological a r X i v : 0 7 1 0 . 5 0 6 5 v 2 [ m a t h . A T ] 2 9 O c t 2 0 0 7 ONDERIVEDCATEGORIESANDDERIVEDFUNCTORS SAMSONSANEBLIDZE Abstract.Foranabeliancategory,acategoryequivalenttoitsderivedcate- goryisconstructedbymeansof...
It is functorial in the sense that exact functors give rise to ‘stable functors’. The notion of a triangle functor (= S-functor [42] = exact functor [12]) appears as the natural axiomatization of this concept. Triangle functors, equivalences and adjoints are presented in Section 8. In...
We study the equivariant category associated to a finite group action on the derived category of coherent sheaves of a smooth projective variety. In partic
The main ingredients of the proofs are as follows: (1) between the derived categories of two module categories, liftable functors coincide with standard functors; (2) any derived equivalence between a module category and an abelian category is uniquely factorized as the composition of a pseudo-...
We prove that such a variety is uniquely determined by its derived category of coherent sheaves. We also calculate the group of exact autoequivalences for these categories. The technics of ample sequences in abelian categories is used.关键词: derived categories coherent sheaves autoequivalences Serre...
The constructions of derived functors providing the triangulated equivalences are based on a generalization of a technique developed in our previous paper arXiv:1503.05523 . 展开 关键词: Mathematics - Category Theory Mathematics - Commutative Algebra Mathematics - Rings and Algebras ...
yieldingaconceptualunificationofMoritatheoryinderivedandbicategoricalcontexts.This ismotivatedbystudyofRickard’stheoremforderivedequivalencesofringsandofMoritatheoryfor ringspectra,whichwepresentinSections2and4.Alongtheway,wegainanunderstandingofthe barrierstoMoritatheoryforDGalgebrasandgiveaconceptualexplanationfor...