Tensor product of sheaves of modules

Depends on

• Modules on a ringed space
• Sheafification of a presheaf

Used by

• h¹ of a line bundle equals the dimension of the space of dual sections Corollary
• The Picard group of the projective line Corollary
• Twisting the exact sequence of an effective Cartier divisor Corollary
• h0 differs from the Euler characteristic before vanishing Counterexample
• The intersection form is not negative definite on all divisor classes Counterexample
• Derived operations on analytic field sheaves Definition
• Flag-variety twisted differential operators and their modules Definition
• Global sections and localization at a fixed infinitesimal character Definition
• Grothendieck groups of coherent sheaves and of vector bundles on a scheme Definition
• Hilbert function and Euler characteristic on a projective scheme Definition
• Hyperelliptic curves and hyperelliptic maps Definition
• Intersection numbers of Cartier divisors on a smooth projective surface Definition
• Multiple test blow-ups, controlled transforms and resolutions of marked ideals Definition
• Picard group of a scheme Definition
• Pullback of a module along a morphism of ringed spaces Definition
• Rational section line bundle Definition
• Symmetric algebra of a quasi-coherent module Definition
• Tensor product of abelian sheaves and its total complex Definition
• The residue pairing of a line bundle with the dual canonical twist Definition
• Twists of a quasi-coherent sheaf Definition
• Twists on the two-affine projective line Example
• Actual analytic constructible sheaves admit coherent six operations Lemma
• Addition and multiplication of marked ideals Lemma
• Addition of Cartier divisors is tensor product of their sheaves Lemma
• Adjunction for a smooth closed subvariety Lemma
• Adjunction formula for effective divisors on a smooth projective surface Lemma
• Ample translation maps split by central-character separation Lemma
• Compact-support acyclicity of c-soft sheaves Lemma
• Derived tensor–Hom and inverse/direct image for field sheaves Lemma
• Dual of a line bundle is its tensor inverse Lemma
• Euler characteristic of a closed point, and invariance under an invertible twist Lemma
• Extensions of line bundles on the projective line split after ordering Lemma
• Finite twisted locally free resolutions on projective space Lemma
• Functoriality of the residue pairing under line-bundle maps and connecting homomorphisms Lemma
• General linear Stiefel approximations stabilize bounded constructible Hom Lemma
• High-degree section module is finite graded Lemma
• Koszul sheaf Ext of a smooth regular immersion is concentrated in codimension Lemma
• Large ample twists of a line bundle are very ample Lemma
• Localization is left adjoint to global sections Lemma
• PBW and integral line-bundle twisting for flag TDOs Lemma

…and 33 more results.

Dependency tree · two levels

6 results within two dependency steps of this one, each drawn at its shortest distance from it. An arrow runs from a result to what uses it, so the chart reads left to right and ends at this result, which carries a heavier outline. Every node is a link to that result. Click elsewhere on the chart to enlarge it.

Sources

• The Stacks Project, Section 17.16 (standard reference, not scraped)
• Ravi Vakil, The Rising Sea, Exercise 2.6.J(a) (standard reference, not scraped)