Talk:Dimension of an algebraic variety

Latest comment: 10 years ago by D.Lazard in topic Field of definition

Field of definition

edit

the article needs to be edited in one of the following two ways:

1. add the assumption that the field K is algebraically closed. 2. explain that some of the definitions are only equivalent if K is algebraically closed (or what definition of "variety," "algebraic set," etc. is being used).

I prefer approach (1). — Preceding unsigned comment added by 128.179.145.222 (talk) 11:59, 28 January 2014 (UTC)Reply

The standard definition of "point of an algebraic variety" is "point with coordinates in an algebraically closed field". This is this standard definition that is implicitly used here. I agree that saying it explicitly is better. It would also be better to say that the dimension does not change if the field K is enlarged or its algebraically closed extension is changed. Also a section about the real dimension (the dimension of the set of real points) would be useful. I have implemented all these clarifications. D.Lazard (talk) 13:18, 28 January 2014 (UTC)Reply