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I am reading Ernst Kunz book, "Introduction to Plane Algebraic Curves"
I need help with some aspects of Kunz' Definition 1.1.
The relevant text from Kunz' book is as follows:View attachment 4556In the above text, Kunz writes the following:
" ... ... If $$K_0 \subset K$$ is a subring and $$\Gamma = \mathscr{V} (f)$$ for a nonconstant polynomial $$f \in K_0 [X,Y]$$ ... ..."
My question is as follows:
Given $$f \in K_0 [X,Y]$$ means that the co-efficients of $$f$$ come from $$K_0$$ ... so if
$$f = aX + bY + c $$
then $$a,b,c$$ come from $$K_0$$ ... that is $$a,b,c \in K_0$$ ... ...
... BUT ... from where do we take the values of $$X$$ and $$Y$$ ... do they likewise come from $$K_0$$ ... or do they come from $$K$$ ...
Hope someone can help clarify this issue ...
Peter
I need help with some aspects of Kunz' Definition 1.1.
The relevant text from Kunz' book is as follows:View attachment 4556In the above text, Kunz writes the following:
" ... ... If $$K_0 \subset K$$ is a subring and $$\Gamma = \mathscr{V} (f)$$ for a nonconstant polynomial $$f \in K_0 [X,Y]$$ ... ..."
My question is as follows:
Given $$f \in K_0 [X,Y]$$ means that the co-efficients of $$f$$ come from $$K_0$$ ... so if
$$f = aX + bY + c $$
then $$a,b,c$$ come from $$K_0$$ ... that is $$a,b,c \in K_0$$ ... ...
... BUT ... from where do we take the values of $$X$$ and $$Y$$ ... do they likewise come from $$K_0$$ ... or do they come from $$K$$ ...
Hope someone can help clarify this issue ...
Peter
Last edited: