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4 votes
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395 views

Do regular noetherian schemes of dimension one only have finitely many etale covers of bounded degree

Let $X$ be a regular noetherian scheme of dimension one. Let $d$ be an integer. Question. Are there only finitely many finite etale morphisms $Y\to X$ of degree $d$? I want to exclude finite etale ...
Masse's user avatar
  • 381
4 votes
1 answer
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Does a curve over a number field have a finite etale cover of given degree

Let $X$ be a (smooth projective geometrically connected) curve over a number field $K$ of genus $g\geq 2$. Let $d\geq 2$ be an integer. Does there exist a curve $Y$ over $K$ with a finite etale $K$-...
Harry's user avatar
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