Alternating group covers of the affine line

For an odd prime p t= 2 mod 3, we prove Abhyankar’s Inertia Conjecture for the alternating group A p +2 , by showing that every possible inertia group occurs for a (wildly ramified) A p +2 -Galois cover of the projective k -line branched only at infinity where k is an algebraically closed field of c...

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Bibliographic Details
Published inIsrael journal of mathematics Vol. 187; no. 1; pp. 117 - 139
Main Authors Muskat, Jeremy, Pries, Rachel
Format Journal Article
LanguageEnglish
Published Heidelberg The Hebrew University Magnes Press 2012
Subjects
Algebra
Analysis
Applications of Mathematics
Group Theory and Generalizations
Mathematical and Computational Physics
Mathematics
Mathematics and Statistics
Theoretical
Galois Extension
Branch Locus
Galois Group
Maximal Subgroup
Projective Line
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Summary:For an odd prime p t= 2 mod 3, we prove Abhyankar’s Inertia Conjecture for the alternating group A p +2 , by showing that every possible inertia group occurs for a (wildly ramified) A p +2 -Galois cover of the projective k -line branched only at infinity where k is an algebraically closed field of characteristic p > 0. More generally, when 2 ≤ s < p and gcd( p −1, s +1) = 1, we prove that all but finitely many rational numbers which satisfy the obvious necessary conditions occur as the upper jump in the filtration of higher ramification groups of an A p + s -Galois cover of the projective line branched only at infinity.
ISSN:0021-2172
1565-8511
DOI:10.1007/s11856-011-0165-7