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If you take the splitting field of $x^5+ax+b$ and consider it as an extension of its quadratic subfield, then it will be unramified with Galois group contained in $A_5$ whenever $4a$ and $5b$ are relatively prime. This is a result of YamamotoYamamoto. For almost all $a$ and $b$ (specifically, on the complement of a thin setthin set), the group is $A_5$.

You might also enjoy this preprintpreprint of Kedlaya, which I found very readable. A note on Kedlaya's webpage, dated May 2003, says that he will not be publishing this because it has been superseded by a recent result of Ellenberg and Venkatesh. I assume he is referring to this paperthis paper, but I can't figure out why that one supersedes his.

If you take the splitting field of $x^5+ax+b$ and consider it as an extension of its quadratic subfield, then it will be unramified with Galois group contained in $A_5$ whenever $4a$ and $5b$ are relatively prime. This is a result of Yamamoto. For almost all $a$ and $b$ (specifically, on the complement of a thin set), the group is $A_5$.

You might also enjoy this preprint of Kedlaya, which I found very readable. A note on Kedlaya's webpage, dated May 2003, says that he will not be publishing this because it has been superseded by a recent result of Ellenberg and Venkatesh. I assume he is referring to this paper, but I can't figure out why that one supersedes his.

If you take the splitting field of $x^5+ax+b$ and consider it as an extension of its quadratic subfield, then it will be unramified with Galois group contained in $A_5$ whenever $4a$ and $5b$ are relatively prime. This is a result of Yamamoto. For almost all $a$ and $b$ (specifically, on the complement of a thin set), the group is $A_5$.

You might also enjoy this preprint of Kedlaya, which I found very readable. A note on Kedlaya's webpage, dated May 2003, says that he will not be publishing this because it has been superseded by a recent result of Ellenberg and Venkatesh. I assume he is referring to this paper, but I can't figure out why that one supersedes his.

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David E Speyer
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If you take the splitting field of $x^5+ax+b$ and consider it as an extension of its quadratic subfield, then it will be unramified with Galois group contained in $A_5$ whenever $4a$ and $5b$ are relatively prime. This is a result of Yamamoto. For almost all $a$ and $b$ (specifically, on the complement of a thin set), the group is $A_5$.

You might also enjoy this preprint of Kedlaya, which I found very readable. A note on Kedlaya's webpage, dated May 2003, says that he will not be publishing this because it has been superseded by a recent result of Ellenberg and Venkatesh. I assume he is referring to this paper, but I can't figure out why that one supersedes his.

If you take the splitting field of $x^5+ax+b$ and consider it as an extension of its quadratic subfield, then it will be unramified with Galois group $A_5$ whenever $4a$ and $5b$ are relatively prime. This is a result of Yamamoto.

You might also enjoy this preprint of Kedlaya, which I found very readable. A note on Kedlaya's webpage, dated May 2003, says that he will not be publishing this because it has been superseded by a recent result of Ellenberg and Venkatesh. I assume he is referring to this paper, but I can't figure out why that one supersedes his.

If you take the splitting field of $x^5+ax+b$ and consider it as an extension of its quadratic subfield, then it will be unramified with Galois group contained in $A_5$ whenever $4a$ and $5b$ are relatively prime. This is a result of Yamamoto. For almost all $a$ and $b$ (specifically, on the complement of a thin set), the group is $A_5$.

You might also enjoy this preprint of Kedlaya, which I found very readable. A note on Kedlaya's webpage, dated May 2003, says that he will not be publishing this because it has been superseded by a recent result of Ellenberg and Venkatesh. I assume he is referring to this paper, but I can't figure out why that one supersedes his.

Source Link
David E Speyer
  • 156.3k
  • 14
  • 421
  • 763

If you take the splitting field of $x^5+ax+b$ and consider it as an extension of its quadratic subfield, then it will be unramified with Galois group $A_5$ whenever $4a$ and $5b$ are relatively prime. This is a result of Yamamoto.

You might also enjoy this preprint of Kedlaya, which I found very readable. A note on Kedlaya's webpage, dated May 2003, says that he will not be publishing this because it has been superseded by a recent result of Ellenberg and Venkatesh. I assume he is referring to this paper, but I can't figure out why that one supersedes his.