Abstract
In Chapter 4 we have assumed that the ground fieldkis algebraically closed. However, if we are interested in the consideration of arithmetic properties of algebraic varieties, we must develop the corresponding theory for the case of non-closed fields such as ℚ or F q .For example, in applying algebraic geometry to coding theory, one should study curves defined over F q and their points with coordinates in F q (such points are called F q -rational).
This is a preview of subscription content, log in via an institution to check access.
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
© 1999 Springer Science+Business Media New York
About this chapter
Cite this chapter
Stepanov, S.A. (1999). Curves over a Finite Field. In: Codes on Algebraic Curves. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-4785-3_5
Download citation
DOI: https://doi.org/10.1007/978-1-4615-4785-3_5
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4613-7167-0
Online ISBN: 978-1-4615-4785-3
eBook Packages: Springer Book Archive