broach
发表于 2025-3-21 18:35:28
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congenial
发表于 2025-3-21 21:53:43
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小步走路
发表于 2025-3-22 04:07:45
Schemes over fields, focus in this and the next chapter on the case of schemes of finite type over a field (although some of the definitions and results are formulated and proved in greater generality). In fact this is also an important building block for the study of arbitrary morphism of schemes . : . → . because we
Misgiving
发表于 2025-3-22 08:24:25
Local Properties of Schemes,ffine space. Compare Figure 1.1: zooming in sufficiently, this is true for the pictured curve in all points except for the point where it self-intersects. However, while in differential geometry this can be used as the definition of a manifold, the Zariski topology is too coarse to capture appropria
北极人
发表于 2025-3-22 08:57:30
Representable Functors,hat we obtain an embedding of the category of schemes into the category of such functors and thus we can consider schemes also as functors. Functors . that lie in the essential image of this embedding are called .. We say that a scheme . . . if .. It is one of the central problems within algebraic g
沉默
发表于 2025-3-22 14:43:35
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Bravura
发表于 2025-3-22 19:58:00
Prevarieties,ynomial equations with coefficients in an arbitrary ring but as a motivation and a guide line we will assume in this chapter that our ring of coefficients is an algebraically closed field .. In this case the theory has a particularly nice geometric flavor.
scrutiny
发表于 2025-3-22 23:19:26
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绊住
发表于 2025-3-23 02:12:41
John Peterson,Elizabeth Bombergundamental for all which follows. Schemes arise by “gluing affine schemes”, similarly as prevarieties are obtained by gluing affine varieties. Therefore after the preparations in the previous chapter, the definition is very simple, see (3.1). As for varieties we define projective space (3.6) by glui
flamboyant
发表于 2025-3-23 05:46:11
An Introduction to the Theory of Games focus in this and the next chapter on the case of schemes of finite type over a field (although some of the definitions and results are formulated and proved in greater generality). In fact this is also an important building block for the study of arbitrary morphism of schemes . : . → . because we