Direct image of a sheaf along a continuous map

Depends on

• A presheaf on a topological space

Used by

• Twisting the exact sequence of an effective Cartier divisor Corollary
• Derived operations on analytic field sheaves Definition
• Geometric vector bundle with the sections convention Definition
• Higher direct image of a sheaf Definition
• Morphisms of ringed spaces Definition
• Adjunction on a smooth plane quartic: the canonical bundle is the hyperplane bundle Example
• Direct image along an open immersion is restriction-compatible intersection Example
• Dualizing and support shifts on the complex line Example
• A sheaf with no stalks off a closed subset is a pushforward Lemma
• Actual analytic constructible sheaves admit coherent six operations Lemma
• Acyclic product fibers stabilize bounded constructible pullback Hom Lemma
• Affine pushforward algebra localizes Lemma
• Affine pushforward is compatible with sheaf cohomology Lemma
• Arithmetic genus, geometric genus and delta invariants Lemma
• Bounded fibrewise-soft resolutions from a uniform all-sheaf dimension bound Lemma
• Cartesian simplicial sheaves model actual equivariant derived Hom Lemma
• Closed immersion preserves cohomology and coherent pushforward Lemma
• Closed immersions are affine quotients and survive base change Lemma
• Cohomology comparison when higher direct images vanish Lemma
• Compact-support calculus along open and closed embeddings Lemma
• Complex algebraic constructible complexes have finite conical cochain models Lemma
• Derived tensor–Hom and inverse/direct image for field sheaves Lemma
• Direct image preserves sheaves and objectwise algebraic structure Lemma
• Euler characteristic of a closed point, and invariance under an invertible twist Lemma
• Extension by zero and the closed complement: a short exact sequence Lemma
• Finite simplicial constructible sheaves have an actual derived incidence model Lemma
• General linear Stiefel approximations stabilize bounded constructible Hom Lemma
• General linear Stiefel perverse normalization is exact and conservative Lemma
• High-degree section module is finite graded Lemma
• Hypersurface cohomology sequence Lemma
• Local-section formula for derived direct image Lemma
• Locally split Cech nerves give actual derived Cartesian sheaf descent Lemma
• Noetherian devissage for coherent proper pushforward Lemma
• Projection formula for a closed immersion and an invertible sheaf Lemma
• Properness survives composition Lemma
• Pushforward along a closed immersion preserves sheaf cohomology Lemma
• Pushouts of closed immersions exist Lemma
• Schematic closure and agreement on a dense open Lemma
• Shifted smooth complex pullback is exact for the middle perverse t structure Lemma
• Structure sheaf of a quasi-compact quasi-separated morphism is affine-local Lemma

…and 22 more results.

Dependency tree · two levels

4 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 6.21: Continuous maps and sheaves (standard reference, not scraped)
• Ravi Vakil, The Rising Sea, Sections 2.2.H and 2.7 (standard reference, not scraped)