Questions tagged [localization]
The localization tag has no usage guidance.
172 questions
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Localisation of injectives
When working with injective modules, one bad thing is that they do not necessarily behave well with respect to localisation. Consider a commutative ring $R$ and have a look at the following properties:...
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(Co)localization of the derived category
Let me start saying that a similar question can be stated for general locally Noetherian Grothendieck categories but I state it for categories of modules as it is simpler. So we fix a right Noetherian ...
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Near-ring localizations
Are there any known results on localization for near-rings (i.e., "rings" with non-abelian addition and only one-sided distributive law)? The books on near-rings I checked don't mention this topic at ...
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Spectra and localizations of the category of topological spaces
Can we construct the category of spectra (or maybe just its homotopy category) from the category of pointed topological spaces
using some kind of localization combined with other categorical ...
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Does Wolbert's derived equivalence between $E_*^R$-local $R$-modules and $R_E$-modules come from a Quillen equivalence?
Let $R$ be a ring spectrum (in the world of EKMM $S$-modules) and let $E$ be a smashing $R$-module. Denote by $R_E$ the $E_*$-localization of $R$. By a theorem of Wolbert (Theorem 2 in Classifying ...
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Localization of quotient rings of polynomials
Working on some Bezout's theorem examples I arrived at a point where I need
$$(\mathbb{K}[x]/(x^2))_{(x)} = \mathbb{K}[x]/(x^2)$$
(i.e. localize don't do anything)($\mathbb{K}$ alg. closed and nice ...
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Homotopical descent information contained in the Dwyer-Kan function complexes of a presheaf category?
Recall that the category of sheaves on some site $C$ equipped with a grothendieck topology $\tau$ is equivalent to the localization of the category of presheaves $W^{-1}Psh(C)$ at $W$ where $W$ is the ...
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Localisation of inclusion functors
Let $\mathcal C$ be a category and suppose $\cal B \subseteq C$ is a full subcategory. Let $i \colon \mathcal B \longrightarrow \cal C$ denote the inclusion functor. Suppose that $S \subseteq \...
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Are these connecting homomorphisms commutative?
Are the connecting homomorphism induced by Kummer sequence and that of localization sequence commutative?
In other words, is the following statement true?
If it is true, then, how can one prove it?
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What is the localization of Q[x]/(x) at 0
Q is a rational field. Q[x] is polynomial ring over Q 。(x) is maximal ideal of Q[x].
Take Q[x]/(x) as a module over Q[x]. Then what is Q[x]-module Q[x]/(x) localize at 0??
I think the result is
Q[x]/...
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Weak equivalences of left Bousfield localizations
Suppose C is a complete and cocomplete category with two model structures (C0,F0,W0) and (C1,F1,W1) such that C0⊃C1, F0⊂F1, W0⊂W1.
If necessary, the model structures can be assumed to be simplicial, ...
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Eigenvector localizaiton
I have raised this sort of question before but I think that now I've found a better term for the subject, one which might ring more bells for people - hence the repost. Hope you won't be too angry ...
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Topological Localization of (the simply-connected cover of) SO or Spin
This is essentially a (cw) reference request, because it seems like the sort of thing that should have been looked at already.
Setting aside, for now, how to think what the localization of a general ...
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Checking locally whether a homomorphism is a localization
All rings below are commutative with $1$.
Suppose $A\subset B$ is a subring and that $A\rightarrow A'$ is a faithfully flat ring homomorphism. [You may assume the rings are actually ${\mathbb C}$-...
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The multiplicative system in a symmetric monoidal category
Let $\mathcal{C}$ be a symmetric monoidal category. In the 1973 paper "Note on monoidal localisation" by Brian Day, the multiplicative system of morphism in $\mathcal{C}$ has been discussed. See also ...
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Rig of fractions, including zero denominators
For some integral domain $R$, one forms the field of fractions $R^*$ by considering (equivalence classes of) formal pairs {$r/s : r \in R, s\in R\backslash 0$} and defining $+$ and $*$ as you'd expect ...
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Controlling Reflective Subcategories and Localizations
Localizations are an extremely important part of modern homotopy theory. Both the category of spaces an spectra have a plethora of interesting localizations: at a fixed prime, rational, with respect ...
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Localization of module
M an A-module, $S\subset A$ a multiplicative subset. Is it possible for $S^{-1}M$ to have an $S^{-1}A$-module structure satisfying $\frac{a}{1}\cdot\frac{m}{1}=\frac{am}{1}$ other than the "usuall" ...
- 2,857
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Ring properties which can be checked on sufficiently many Ore localizations
Let $R$ be a non-commutative Ore domain, and let $R[S_i^{-1}]$ be a finite set of Ore localizations. The absence of a geometric theory means there is no obvious candidate for when this set of ...
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Localization of power series and module structure
Let $R=\mathbb{Q}[X,Y]$ be the polynomial ring of two commuting variable.
Let $S$ be the multiplicative subset of $R$ generated by homogeneous linear polynomials.
Let also $\widehat{R}$ be the ring of ...
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Flatness of module
$A\rightarrow B$ a ring homomorphism, $N$ a $B$-module which is flat over $A$. $\mathfrak{q}\subset B$ a prime ideal, $\mathfrak{p}\subset A$ its contraction in $A$. Then is it true that $N_{\mathfrak{...
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Computing morphisms in localizations of $K(B)$
Let $B$ be an additive category (a small one; one can assume that it is a $\mathbb{Q}$-category, yet not much else is known about it). Given a set of objects $S$ of $K^b(B)$ (or $K(B)$), I consider ...
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