Publication Type |
dissertation |

School or College |
College of Science |

Department |
Mathematics |

Author |
Kocs, Christopher |

Title |
Construction of 2-ADIC Galois extension with wild inertia given by an extra special 2-group |

Date |
2012-08 |

Description |
Given any field F and an odd integer n, suppose K be a degree 2n1 multiquadratic extension of F. We consider the conditions under which there is a Galois extension E of F such that Gal(E/F) is a particular extra special 2-group T0 { namely, the multiplicative group generated by basis elements of the even Clifford algebra associated with the quadratic form X2 1 + ::: + X2 n. These conditions can be restated in terms of the Weil index, which can be computed explicitly as a Gauss sum when F = Q2n. We prove an equidistribution of Gauss sums for quadratic characters on Q2n of conductor 4Z2n. As a consequence, we prove that, when n is an odd prime greater than 3, there exists a Galois extension K of Q2 such that K is a multiquadratic extension of Q2n that admits a quadratic extension E such that Gal(E/F) = T0. |

Type |
Text |

Publisher |
University of Utah |

Subject |
2-adic field extensions; Clifford algebra; Elliptic curve; Extra special 2-group; Galois theory; Quadratic forms |

Subject LCSH |
Galois cohomology |

Dissertation Institution |
University of Utah |

Dissertation Name |
Doctor of Philosophy |

Language |
eng |

Rights Management |
Copyright © Christopher Kocs 2012 |

Format Medium |
application/pdf |

Format Extent |
393,300 bytes |

Identifier |
etd3/id/1848 |

Source |
Original in Marriott Library Special Collections, QA3.5 2012 .K63 |

ARK |
ark:/87278/s63t9z0q |

Setname |
ir_etd |

Date Created |
2012-08-20 |

Date Modified |
2017-10-02 |

ID |
195536 |

Reference URL |
https://collections.lib.utah.edu/details?id=195536 |