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Jun 20, 2012 at 8:30 comment added S. Carnahan In your "we know that" sentence, you really need the fields of transcendence degree 1 to be finitely generated.
Jun 19, 2012 at 16:21 comment added Francesco Polizzi Hartshorne, Chapter I, Section 4
Jun 19, 2012 at 16:18 answer added user19475 timeline score: 4
Jun 19, 2012 at 16:15 comment added expmat Is this a functorial equivalence? Where can I read about this?
Jun 19, 2012 at 16:14 comment added Francesco Polizzi For algebraic varieties the transcendence degree of the function field is equal to the dimension, so the answer is yes: just replace $1$ with $n := \dim X$
Jun 19, 2012 at 16:07 history edited expmat CC BY-SA 3.0
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Jun 19, 2012 at 16:02 history asked expmat CC BY-SA 3.0