Cohomology of Sheaves

Iversen, B. (1986). Cohomology of Sheaves. Springer.

Type

Book

Intellectual base

Review or monograph

Year

1986

DOI

10.1007/978-3-642-82783-9

ISBN

9783540163893

DOI registrant

Springer Nature

Link

https://doi.org/10.1007/978-3-642-82783-9

Cited by

3 citations across 2 artifacts.

Domain-specific

• Direct image with compact support
  • The direct image with compact support \(f_!\mathcal F\) is the subsheaf of \(f_*\mathcal F\) whose sections over \(U\subseteq Y\) have support mapping properly to (U); in the locally compact Hausdorff setting this is the standard proper-support direct image.
• Inverse image functor
  • Inverse image for sheaves is not merely sectionwise precomposition, sheafification is generally required, direction is contravariant in spaces but the functor itself maps Sh(Y) to Sh(X) and for ringed spaces module pullback adds tensor product.
  • … of f(U), sheafification, inverse-image sheaf f inverse G, action on morphisms, stalk isomorphism at x, adjunction with direct image and exactness and module or ringed-space variant are explicit. to An applied instance preserves the invariant under changed notation, scale, dataset, jurisdiction, or implementation..

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