Difference between revisions of "Pseudo algebraically closed field"
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| − | A field $K$ for which every non-empty [[algebraic variety]] defined over $K$ has a $K$-rational point. Clearly an [[algebraically closed field]] is PAC. The Brauer group of a | + | A field $K$ for which every non-empty [[algebraic variety]] defined over $K$ has a $K$-rational point. Clearly an [[algebraically closed field]] is PAC. The Brauer group of a PAC field is trivial. |
See also [[Quasi-algebraically closed field]]. | See also [[Quasi-algebraically closed field]]. | ||
Revision as of 13:33, 30 December 2015
A field $K$ for which every non-empty algebraic variety defined over $K$ has a $K$-rational point. Clearly an algebraically closed field is PAC. The Brauer group of a PAC field is trivial.
See also Quasi-algebraically closed field.
References
- Fried, Michael D.; Jarden, Moshe Field arithmetic (3rd revised ed.) Ergebnisse der Mathematik und ihrer Grenzgebiete. 3e Folge 11 Springer (2008) ISBN 978-3-540-77269-9 Zbl 1145.12001
How to Cite This Entry:
Pseudo algebraically closed field. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Pseudo_algebraically_closed_field&oldid=37154
Pseudo algebraically closed field. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Pseudo_algebraically_closed_field&oldid=37154