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Tuesday 12 January 2010, 14:30-15:30
Non-solvable Galois number fields ramified at 2, 3 and 5 only
- đ¤ Speaker: Lassina Dembele (Warwick)
- đ Date & Time: Tuesday 12 January 2010, 14:30 - 15:30
- đ Venue: MR13
Abstract
In the mid 90s, Dick Gross made the following conjecture.
Conjecture: For every prime p, there exists a non-solvable Galois number field K ramified at p only.
For p >= 11 this conjecture follows from results of Serre and Swinnerton-Dyer using mod p Galois representations attached to classical modular forms. However, it a consequence of the Serre conjecture, now a theorem thanks to Khare and Wintenberger, et al, that classical modular forms cannot yield the case p <= 7. In this talk, we show that the conjecture is true for p = 2, 3 and 5 using Galois representations attached to Hilbert modular forms. We will also explain the limitations of this technique for the prime p = 7, and outline an alternative strategy using the unitary group U(3) attached to the extension Q(zeta_7)/Q(zeta_7)^+.
Series This talk is part of the Number Theory Seminar series.
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