query: Hartshorne, Prop II.5.2(d,e): direct and inverse images of sheaves associated to modules
positive_passages.docid: 28324
positive_passages.text: Inverse image of the sheaf associated to a module
negative_passages.docid: 145700
negative_passages.text: Module isomorphic to second dual
negative_passages.docid: 97669
negative_passages.text: Sheafs and closed immersion
negative_passages.docid: 30465
negative_passages.text: Determining which rings have a module which is not semisimple
negative_passages.docid: 79328
negative_passages.text: Proposition 5.15 from Atiyah and Macdonald: Integral Closure and Minimal Polynomial
negative_passages.docid: 116350
negative_passages.text: First axiom of sheaves: in noetherian topological spaces the direct limit presheaf is a sheaf.
negative_passages.docid: 76432
negative_passages.text: $i^{-1} F$ a sheaf if and only if $\varinjlim_{ U \subseteq X \text{ open}, ~ x,y \in U } F(U) \to F_x \times F_y$ is an isomorphism.
negative_passages.docid: 76318
negative_passages.text: Prove that a presheaf is a sheaf
negative_passages.docid: 101860
negative_passages.text: Relating the normal bundle and trivial bundles of $S^n$ to the tautological and trivial line bundles of $\mathbb{R}P^n$
negative_passages.docid: 126094
negative_passages.text: Hartshorne Algebraic Geometry Exercise II.2.16.
negative_passages.docid: 66866
negative_passages.text: Algebraic dual of $\mathbb{R}^{\mathbb{N}}$
negative_passages.docid: 8654
negative_passages.text: Global sections of $\mathcal{O}(-1)$ and $\mathcal{O}(1)$, understanding structure sheaves and twisting.
negative_passages.docid: 72103
negative_passages.text: Failure of isomorphisms on stalks to arise from an isomorphism of sheaves
negative_passages.docid: 141900
negative_passages.text: Exact sequence and Noetherian modules
negative_passages.docid: 95930
negative_passages.text: Finitely generated modules over a Noetherian ring are Noetherian
negative_passages.docid: 72295
negative_passages.text: A difficulty in understanding the proof of distributivity of tensor products over direct sums for modules.
negative_passages.docid: 47630
negative_passages.text: Endomorphisms of modules satisfying chain conditions and counterexamples.