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expmat
expmat
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We know that (for an algebraically closed field $k$) there is an equivalence between algebraic curves over $k$ (up to birational equivalence) and fields of transcendence degree 1$1$ over $k$.

Is there something similar for higher dimensional algebraic varieties?

We know that (for an algebraically closed field $k$) there is an equivalence between algebraic curves over $k$ (up to birational equivalence) and fields of transcendence degree 1 over $k$.

Is there something similar for higher dimensional algebraic varieties?

We know that (for an algebraically closed field $k$) there is an equivalence between algebraic curves over $k$ (up to birational equivalence) and fields of transcendence degree $1$ over $k$.

Is there something similar for higher dimensional algebraic varieties?

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expmat
expmat
  • 1.3k
  • 14
  • 26

Function fields <-> curves (and beyond)

We know that (for an algebraically closed field $k$) there is an equivalence between algebraic curves over $k$ (up to birational equivalence) and fields of transcendence degree 1 over $k$.

Is there something similar for higher dimensional algebraic varieties?