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Erik Walsberg
Erik Walsberg
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Well, thanks everyone, but in the end I found a a good reference. I will post it here as this might be useful for someone else.

The following is (a special case of) Corollary 5.4.3 in Mumford and Oda's Algebraic Geometry II: Suppose that $V$ and $W$ are integral $K$-varieties, $W$ is regular, and $f : V \to W$ is a dominant morphism. Then $f$ is smooth on a dense open subset of $V$ if and only if the function field of $V$ is a separable extension of the function field of $W$. The result in the book is written for schemes.

Well, thanks everyone, but in the end I found a a good reference. I will post it here as this might be useful for someone else.

The following is (a special case of) Corollary 5.4.3 in Mumford and Oda's Algebraic Geometry II: Suppose that $V$ and $W$ are integral $K$-varieties, $W$ is regular, and $f : V \to W$ is a dominant morphism. Then $f$ is smooth on a dense open subset of $V$ if and only if the function field of $V$ is a separable extension of the function field of $W$.

Well, thanks everyone, but in the end I found a good reference. I will post it here as this might be useful for someone else.

The following is (a special case of) Corollary 5.4.3 in Mumford and Oda's Algebraic Geometry II: Suppose that $V$ and $W$ are integral $K$-varieties, $W$ is regular, and $f : V \to W$ is a dominant morphism. Then $f$ is smooth on a dense open subset of $V$ if and only if the function field of $V$ is a separable extension of the function field of $W$. The result in the book is written for schemes.

Source Link
Erik Walsberg
Erik Walsberg
  • 1.7k
  • 9
  • 20

Well, thanks everyone, but in the end I found a a good reference. I will post it here as this might be useful for someone else.

The following is (a special case of) Corollary 5.4.3 in Mumford and Oda's Algebraic Geometry II: Suppose that $V$ and $W$ are integral $K$-varieties, $W$ is regular, and $f : V \to W$ is a dominant morphism. Then $f$ is smooth on a dense open subset of $V$ if and only if the function field of $V$ is a separable extension of the function field of $W$.