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Sean Lawton
Sean Lawton
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This question probably follows from standard geometric invariant theory. If true I'd to know a reference for it. 

Given a projective scheme $X\rightarrow S$ over the base $S$. Let's assume a finite group $G$ is acting on $X$ and its quotient is an $S$-scheme $X//G$. 

Is the quotient projective or at least proper? (I have seen versions of this over fields but not for arbitrary base.)

This question probably follows from standard geometric invariant theory. If true I'd to know a reference for it. Given a projective scheme $X\rightarrow S$ over the base $S$. Let's assume a finite group $G$ is acting on $X$ and its quotient is an $S$-scheme $X//G$. Is the quotient projective or at least proper? (I have seen versions of this over fields but not for arbitrary base.)

This question probably follows from standard geometric invariant theory. If true I'd to know a reference for it. 

Given a projective scheme $X\rightarrow S$ over the base $S$. Let's assume a finite group $G$ is acting on $X$ and its quotient is an $S$-scheme $X//G$. 

Is the quotient projective or at least proper? (I have seen versions of this over fields but not for arbitrary base.)

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user127776
user127776
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Is quotient of projective scheme over arbitrary base by a finite group also projective

This question probably follows from standard geometric invariant theory. If true I'd to know a reference for it. Given a projective scheme $X\rightarrow S$ over the base $S$. Let's assume a finite group $G$ is acting on $X$ and its quotient is an $S$-scheme $X//G$. Is the quotient projective or at least proper? (I have seen versions of this over fields but not for arbitrary base.)