منابع مشابه
Math 233a Final Presentation: Serre Duality for Projective Spaces
Let V be a vector space of dimension n+1 over a field k, and consider the scheme X = PV ∼= Pk ∼= Proj(k[x0, . . . , xn]). Consider F a quasi-coherent sheaf over X. We can examine its Cech cohomology which coincides with its sheaf (nonetale) cohomology because X is Noetherian and separated (cf. Hartshorne, ch. III theorem 4.5.). Particularly, H(X,F) ∼= Γ(F , X). However Γ(F , X) ∼= HomX(OX ,F). ...
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We introduce the generalized Serre functor S on a skeletally-small Hom-finite Krull-Schmidt triangulated category C. We prove that its domain Cr and range Cl are thick triangulated subcategories. Moreover, the subcategory Cr (resp. Cl) is the smallest additive subcategory containing all the objects in C which appears as the third term (resp. the first term) of some Aulsander-Reiten triangle in ...
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We carefully develop the theory of Serre duality and dualizing sheaves. We differ from the approach in [12] in that the use of spectral sequences and the Yoneda pairing are emphasized to put the proofs in a more systematic framework. As applications of the theory, we discuss the RiemannRoch theorem for curves and Bott’s theorem in representation theory (following [8]) using the algebraic-geomet...
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We introduce sheaves and sheaf cohomology and use them to prove the Riemann-Roch theorem and Serre duality. The main proofs follow the treatment in Forster [3].
متن کاملSerre Duality for Non-commutative P-bundles
Abstract. Let X be a smooth scheme of finite type over a field K, let E be a locally free OX -bimodule of rank n, and let A be the non-commutative symmetric algebra generated by E. We construct an internal Hom functor, HomGrA(−,−), on the category of graded right A-modules. When E has rank 2, we prove that A is Gorenstein by computing the right derived functors of HomGrA(OX ,−). When X is a smo...
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ژورنال
عنوان ژورنال: Advances in Mathematics
سال: 2017
ISSN: 0001-8708
DOI: 10.1016/j.aim.2016.10.013