Abstract
A very important special case are schemes that are of finite type over a field. Thus before we progress with the general abstract theory of schemes we 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 f : X → S because we have seen how we may attach to each s ∈ S its fiber Xs = f−1 (s) (4.8). Thus f yields a family of schemes over various fields and we may study f by first studying its fibers and then how these fibers vary.
Keywords
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2010 Vieweg+Teubner Verlag | Springer Fachmedien Wiesbaden
About this chapter
Cite this chapter
Görtz, U., Wedhorn, T. (2010). Schemes over fields. In: Algebraic Geometry I. Vieweg+Teubner. https://doi.org/10.1007/978-3-8348-9722-0_6
Download citation
DOI: https://doi.org/10.1007/978-3-8348-9722-0_6
Publisher Name: Vieweg+Teubner
Print ISBN: 978-3-8348-0676-5
Online ISBN: 978-3-8348-9722-0
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)