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there is a time I know, but I have already forgot it. Now, my brain just does not work. You need a text book. By the way, is this field finite? in total how many elements for its set? it will be great to mention it in the article. Though in its above text, we can see "finitely generated".
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just a note: I got to know related stuff when I was counting the order of an elliptic curve, and do Tate paring. I have to go back to read those related stuff to answer my current curious question whether the function field is finite.
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I am new in these concepts but the last phrase " Its function field is the field K(x,y), generated by elements x and y that are transcendental over K and satisfy the algebraic relation
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