Titlebook: Algebraic Geometry; Part I: Schemes. Wit Ulrich Görtz,Torsten Wedhorn Textbook 20101st edition Vieweg+Teubner Verlag | Springer Fachmedien

Hallowed

Collective Decisions under UncertaintyIn this chapter we study one of the central technical tools of algebraic geometry: If . is a scheme and . and . are .-schemes we define the product . ×. . of . and . over . which is also called fiber product. We do this by defining . ×. . as an .-scheme which satisfies a certain universal property (and by proving that such a scheme always exists).

机械

Computer-Based Information SystemsRecall that a topological space . is .ausdorff if and only if the following equivalent conditions are satisfied.

sperse

https://doi.org/10.1007/978-981-13-2871-8In this chapter, we will study properties of morphisms of schemes which distinguish important subclasses of morphisms. The emphasis in this chapter is on properties that are . local on the source. We start with a relative version of being affine and then study finite and quasi-finite morphisms.

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Sonia Camacho,Andrea Herrera,Andrés BarriosIn this chapter we will apply the results obtained so far to noetherian schemes of dimension one. Arbitrary one-dimensional noetherian schemes will be .. Examples for absolute curves are rings of integers in number fields (i.e., finite extensions of ℚ) or schemes of finite type over a field . of pure dimension one. The latter we will ..

tolerance

Gloria Urrea,Alfonso J. Pedraza-MartinezIn this chapter we consider several examples. Each example is given in such a way that it progresses along the theory introduced in the book and that it is possible to study the examples in parallel to the main text. We indicate in the section titles up to which chapter definitions and results are used in that particular section.

说笑

泥沼

adulterant

钝剑

Affine and proper morphisms,In this chapter, we will study properties of morphisms of schemes which distinguish important subclasses of morphisms. The emphasis in this chapter is on properties that are . local on the source. We start with a relative version of being affine and then study finite and quasi-finite morphisms.

山顶可休息

One-dimensional schemes,In this chapter we will apply the results obtained so far to noetherian schemes of dimension one. Arbitrary one-dimensional noetherian schemes will be .. Examples for absolute curves are rings of integers in number fields (i.e., finite extensions of ℚ) or schemes of finite type over a field . of pure dimension one. The latter we will ..