query: Why are the global sections of structure sheaf of Proj$S$ just the homogenous elements of $S$?
positive_passages.docid: 155445
positive_passages.text: What kind of ring $R$ makes $\mathcal O(\mathrm{Proj}\,R[x_0,\cdots,x_n])=R$?
negative_passages.docid: 86224
negative_passages.text: The root system of $sl(3,\mathbb C)$
negative_passages.docid: 56647
negative_passages.text: Structure of $Gal(\mathbb{Q}(\zeta_{15})/\mathbb{Q})$?
negative_passages.docid: 143138
negative_passages.text: All models of $\mathsf{ZFC}$ between $V$ and $V[G]$ are generic extensions of $V$
negative_passages.docid: 74259
negative_passages.text: Why is the localization of a commutative Noetherian ring still Noetherian?
negative_passages.docid: 152200
negative_passages.text: Is the space of smooth sections of a vector bundle finitely generated as a $C^\infty$-module?
negative_passages.docid: 115502
negative_passages.text: Analogue of the Cantor-Bernstein-Schroeder theorem for general algebraic structures
negative_passages.docid: 73689
negative_passages.text: A question about the equivalence relation on the localization of a ring.
negative_passages.docid: 96380
negative_passages.text: Representation of $\text{sl}(2,\mathbb{C})$
negative_passages.docid: 147133
negative_passages.text: If a morphism has a section then it is an effective epimorphism?
negative_passages.docid: 142699
negative_passages.text: Is $R/N(R)$ a faithfully flat $R$-module?
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: 83109
negative_passages.text: Formation of the free group on $S$ is a functor
negative_passages.docid: 39652
negative_passages.text: Quotient of free module
negative_passages.docid: 118288
negative_passages.text: Complex structure on $\mathbb S^1 \times \mathbb S^3$
negative_passages.docid: 38571
negative_passages.text: Localization of a total quotient ring of a reduced ring
negative_passages.docid: 40427
negative_passages.text: Presheaf image of a monomorphism of sheaves is a sheaf