Sheaves of super algebras and tensor products.
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Special Sheaves of Algebras : SSA Sheaves of tensor algebras, symmetric algebras, exterior algebras, polynomial algebras and ideal products. Complete study of these constructions as adjoints. Modules over a Scheme : MOS Ideals, special functors extension by zero and coextension of scalars , locally free sheaves, sheaf Hom, extension of coherent sheaves.
K-Theory Notes 9 - Lecture 009 21 Some algebra ltered and...
The Proj Construction : TPC Functorial properties, products, linear morphisms, projective morphisms, dimensions of some schemes, points of projective space. Relative Affine Schemes : RAS Affine morphisms, the Spec construction, the sheaf associated to a sheaf of quasi-coherent modules over an algebra.
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Concentrated Schemes : CON Basic properties of quasi-compact and quasi-separated schemes and morphisms. In our notes a quasi-compact quasi-separated morphism or scheme is called concentrated. Section 2.
Section 3. A vanishing theorem of grothendieck, cohomology of noetherian schemes, Cech cohomology, the cohomology of projective space, Ext groups and sheaves. Definition of the higher coinverse image functors, and their properties. Direct image and quasi-coherent sheaves, uniqueness of cohomology. The sheaf associated to a sheaf of graded modules, the graded module associated to a quasi-coherent sheaf, functorial properties, ideal sheaves and closed subschemes, the duple embedding, twisting with invertible sheaves.
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Schemes via Noncommutative Localisation : SFL Gabriel topologies and localisation with respect to them, the situation for commutative rings and how this relates to algebraic geometry. In Chapter C we derive some structural results relating to the graded properties of the rings considered. The following classes of graded rings receive special attention: fully bounded Noetherian rings, birational extensions of commutative rings, rings satisfying polynomial identities, and Von Neumann regular rings. Here the basic idea is to derive results of ungraded nature from graded information.
Some of these sections lead naturally to the study of sheaves over the projective spectrum Proj R of a positively graded ring, but we did not go into these topics here. We refer to  for a noncommutative treatment of projective geometry, i. Bloggat om Graded Ring Theory. See details. See all 2 brand new listings.go here
Graded and Filtered Rings and Modules - Constantin Năstăsescu, F. Van Oystaeyen - Google книги
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Graded and Filtered Rings and Modules
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