Galois extensions ramified at one prime

Jing Long Hoelscher, University of Pennsylvania


This thesis studies Galois extensions of global fields and associated Galois groups with one ramified prime, in both the number field and function field cases. Over Q some restrictions on both solvable and nonsolvable Galois groups ramified only at one prime are shown. We also give a description of tamely ramified meta-abelian Galois groups and examples of infinite class field towers with one finite prime ramified. Over real quadratic fields Q&parl0;d&parr0; , results about nilpotent Galois groups ramified only at one prime in Q&parl0;d&parr0; are shown. Over function fields F q(t), a stronger version of the forward direction of “Abhyankar's conjecture” is proved. Finally, we give a simple description of cyclotomic function fields with a view toward developing Iwasawa theory for cyclotomic function fields. ^

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Recommended Citation

Long Hoelscher, Jing, "Galois extensions ramified at one prime" (2007). Dissertations available from ProQuest. AAI3260949.