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- abstract algebra - stalk is identified with the localization of the . . .
By the universal property of localization, if we can show that each $f \not \in m_p$ is invertible in $\mathcal {O}_p$, then we'll get a (unique!) map $\mathcal {O} (X)_ {m_p} \to \mathcal {O}_ {p}$
- Derived categories and algebraic geometry
Inspired by work on the stable homotopy category (description of the chromatic tower), Hopkins and Neeman [Ho, Neel] have given a classification of thick subcategories of the category of perfect complexes over an affine variety
- Derived category - Wikipedia
Despite the level of abstraction, derived categories became accepted over the following decades, especially as a convenient setting for sheaf cohomology Perhaps the biggest advance was the formulation of the Riemann–Hilbert correspondence in dimensions greater than 1 in derived terms, around 1980
- DERIVED CATEGORIES Contents - Columbia University
1 Introduction in triangulated categories Next, we prove that the homotopy category of complexes in an additive category is a triangulated category Once this is done we define the derived category of an abelian category as the localization of the homotopy category with re pect to quasi-isomorphisms A good reference is Ve dier’s thesis [Ver96]
- Lectures on Derived Categories Dragan Mili ci c - University of Utah
2 Localization of additive categories 2 1 Localization of an additive category Assume now that A is an ad-ditive category and that S is a localizing class of morphisms in A
- Localization of Categories (Chapter 6) - Derived Categories
In this section we take a close look at localization of categories Let K be an abstract category (i e without any extra structure), and let S ⊆ K be a multiplicatively closed set of morphisms
- Derived Categories - Merrick Cai
In fact, they are precisely the adjoints of the inclusions of categories: τ≤N is the right adjoint to the inclusion D≤N ,→ D, and τ≥N is the left adjoint to the inclusion D≥N ,→ D
- Descent conditions for generation in derived categories
This work establishes a condition that determines when strong generation in the bounded derived category of a Noetherian J 2 scheme is preserved by the derived pushforward of a proper morphism
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