Wild ramification bounds and simple group galois extensions ramified only at 2

John Jones

doi:10.1090/S0002-9939-2010-10628-7

Wild ramification bounds and simple group galois extensions ramified only at 2

John Jones

Mathematical and Statistical Sciences, School of (SoMSS)

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

Abstract

We consider finite Galois extensions of Q_p and deduce bounds on the discriminant of such an extension based on the structure of its Galois group. We then apply these bounds to show that there are no Galois extensions of Q, unramified outside of {2,∞}, whose Galois group is one of various finite simple groups. The set of excluded finite simple groups includes several infinite families.

Original language	English (US)
Pages (from-to)	807-821
Number of pages	15
Journal	Proceedings of the American Mathematical Society
Volume	139
Issue number	3
DOIs	https://doi.org/10.1090/S0002-9939-2010-10628-7
State	Published - Mar 2011

ASJC Scopus subject areas

General Mathematics
Applied Mathematics

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10.1090/S0002-9939-2010-10628-7

Cite this

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abstract = "We consider finite Galois extensions of Qp and deduce bounds on the discriminant of such an extension based on the structure of its Galois group. We then apply these bounds to show that there are no Galois extensions of Q, unramified outside of \{2,∞\}, whose Galois group is one of various finite simple groups. The set of excluded finite simple groups includes several infinite families.",

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AB - We consider finite Galois extensions of Qp and deduce bounds on the discriminant of such an extension based on the structure of its Galois group. We then apply these bounds to show that there are no Galois extensions of Q, unramified outside of {2,∞}, whose Galois group is one of various finite simple groups. The set of excluded finite simple groups includes several infinite families.

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UR - https://www.scopus.com/pages/publications/79951828914#tab=citedBy

U2 - 10.1090/S0002-9939-2010-10628-7

DO - 10.1090/S0002-9939-2010-10628-7

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Wild ramification bounds and simple group galois extensions ramified only at 2

Abstract

ASJC Scopus subject areas

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