Support of a sheaf
WebAug 23, 2024 · Let F be a coherent sheaf on a locally Noetherian scheme X. We define the annihilator A n n ( F) of F to be A n n ( F) ( U) := { f ∈ O X ( U) ∀ x ∈ U, ∀ m x ∈ F x, f ⋅ m x = 0 } for any open set U ⊂ X. (Liu defines it differently, to be the kernel of the sheaf morphism α: O X → H o m O X ( F, F)) WebMeaning of sheaf in English. sheaf. noun [ C ] uk / ʃiːf / us / ʃiːf / plural sheaves. a number of things, especially pieces of paper or plant stems, that are held or tied together: A lawyer …
Support of a sheaf
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If F is a quasicoherent sheaf on a scheme X, the support of F is the set of all points x in X such that the stalk Fx is nonzero. This definition is similar to the definition of the support of a function on a space X, and this is the motivation for using the word "support". Most properties of the support generalize from modules to quasicoherent sheaves word for word. For example, the support of a coherent sheaf (or more generally, a finite type sheaf) is a closed subspace of X. WebJun 6, 2024 · Tour Start here for a quick overview of the site Help Center Detailed answers to any questions you might have Meta Discuss the workings and policies of this site
WebApr 15, 2016 · Support of a Coherent Sheaf and Noetherianity. 5. Tensor product of faithful modules. 6. Support of a module and submodule. 3. Tensor product of two cyclic modules. 9. Annihilator of a flat module and faithfully flatness. 4. A module with infinitely many associated primes. 4. WebYou can also dene the sheaf of non-commutative algebras T F, the sheaf of commuta-tive algebras Sym F, and the sheaf of skew-commutative algebras ^ F. 1.D. EXERCISE …
WebFor an abelian sheaf on a topological space we have discussed the subsheaf of sections with support in a closed subset in Modules, Remark 17.6.2. For quasi-coherent modules this submodule isn't always a quasi-coherent module, but if the closed subset has a retrocompact complement, then it is. Lemma 28.24.5. Let be a scheme. Let be a closed …
WebThe support of a presheaf Fon Xis the closed subset suppF:= fx2XjF x6= 0 g: The support of a section s2F(U) is the closed set supp(s) = fx2Ujs x6= 0 g: Under the heuristic that …
Web6.17 Sheafification In this section we explain how to get the sheafification of a presheaf on a topological space. We will use stalks to describe the sheafification in this case. This is different from the general procedure described in Sites, Section 7.10, and perhaps somewhat easier to understand. The basic construction is the following. infiniti intouch navigationWebThe definition in Hartshorne is that the support is simply the set of points at which the stalk is nonzero. What you've stated here will be the closure of that set. It's often the case, as in … infiniti in orland parkWebStack Exchange network consists of 181 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and … infiniti intouch services premierWebSheaf. Bundle of grain. And he said unto them, Hear, I pray you, this dream which I have dreamed: for, behold, we were binding sheaves in the field, and, lo, my SHEAF arose, and … infiniti interior touch up paintWebNov 3, 2024 · You are doing a mistake many beginners do, when learning modern algebraic geometry. The support of a section of a sheaf must not be interpreted as the support of a function. If you interpret a section of a sheaf as a function, its zeroes must be interpreted as the set of points, where the stalk is contained in the maximal ideal. infiniti iowa cityWebMay 6, 2024 · Let X and Y be topological spaces and let f: X → Y be a continuous map. Let F be a sheaf of abelian groups on X. For a section σ of F the support of σ is defined to be the closure of { x ∣ σ x ≠ 0 }. The proper direct image f! F is then defined to be the sheaf on Y with f! infiniti interior ceiling lightWebApr 14, 2024 · Bring your own builder and build your dream home. Just a quick drive south to Hamilton, this lot gives your future home that rural neighborhood location with a short commute to town. Call Dave Wells at 406-640-1279, or your real estate professional. Listed by David Wells • PureWest Real Estate (06231615) - Missoula. infiniti intouch customer service