WebMay 15, 2024 · Given small dg categories A and B and a B-A-bimodule T, we give necessary and sufficient conditions for the associated derived functors of Hom and the tensor product to be fully faithful. Special emphasis is put on the case when RHom $$_\\mathrm{A}$$ A (T,?) is fully faithful and preserves compact objects, in which case … WebA tilting complex T over A is an object in Kb(P(A)) which satisfies the following conditions: (I) for all i ≠ 0, the set HomDb(A)(T, T[i]) of homomorphisms in Db(A) vanishes, (II) the category add(T) (that is, the full subcategory of all direct sums of direct summands of T inside Kb(P(A))) generates Kb(P(A)) as a triangulated category.

Fourier-Mukai transforms (Chapter 7) - Handbook of Tilting Theory

WebMay 25, 2010 · The first non-trivial derived equivalence in the literature is between the derived categories of sheaves on a sphere bundle and its dual bundle [70]. The … Web2004. Abstract. We review the basic definitions of derived categories and derived functors. We illustrate them on simple but non trivial examples. Then we explain Happel's theorem … high tide oc md

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WebMay 25, 2010 · We review the basic definitions of derived categories and derived functors. We illustrate them on simple but non trivial examples. Then we explain Happel's theorem which states that each tilting triple yields an equivalence between derived categories. WebWe review the basic definitions of derived categories and derived functors. We illustrate them on simple but non trivial examples. Then we explain Happel’s theorem which … Web7.6 The Opposite Derived Category Is Triangulated 183. Cambridge University Press 978-1-108-41933-8 — Derived Categories Amnon Yekutieli Frontmatter ... 14 Perfect and Tilting DG Modules over NC DG Rings 373 14.1 Algebraically Perfect DG Modules 373 14.2 Derived Morita Theory 387 how many doors in a house