Dembélé, Lassina (2009) Nonsolvable Galois number fields ramified at 2, 3 and 5 only. In: Invited Speaker : London Number Theory Seminar, Imperial College, London, 28 Oct 2009 (Unpublished)

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Abstract

In the mid 90s, Dick Gross proposed the following conjecture.
Conjecture: For every prime p, there is a nonsolvable Galois number field K ramified at p only. For p>=11, this conjecture is a consequence of results of Serre and Deligne (using classical modular forms). In this talk, we will show that the conjecture is true for p=2, 3 and 5. The extensions K we constructed in those cases are obtained by using Galois representations attached to Hilbert modular forms. We will also outline a strategy to tackle the case p=7 using automorphic forms on U(3).

Item Type:	Conference Item (Paper)
Subjects:	Q Science > QA Mathematics
Divisions:	Faculty of Science, Engineering and Medicine > Science > Mathematics
Official Date:	28 October 2009
Dates:	Date Event 28 October 2009 Completion
Status:	Not Peer Reviewed
Publication Status:	Unpublished
Conference Paper Type:	Paper
Title of Event:	Invited Speaker : London Number Theory Seminar, Imperial College
Type of Event:	Other
Location of Event:	London
Date(s) of Event:	28 Oct 2009

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