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SUMMARY:Non-solvable Galois number fields ramified at 2\, 3 and 5 only - L
 assina Dembele (Warwick)
DTSTART:20100112T143000Z
DTEND:20100112T153000Z
UID:TALK22115@talks.cam.ac.uk
CONTACT:Tom Fisher
DESCRIPTION:In the mid 90s\, Dick Gross made the following conjecture.\n\n
 \nConjecture: For every prime _p_\, there exists a non-solvable Galois num
 ber field _K_ ramified at _p_ only.\n\n\nFor _p_ >= 11 this conjecture fol
 lows from results of Serre and Swinnerton-Dyer using mod _p_ Galois repres
 entations 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 t
 his 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 ex
 plain the limitations of this technique for the prime _p_ = 7\, and outlin
 e an alternative strategy using the unitary group U(3) attached to the ext
 ension *Q*(zeta_7)/*Q*(zeta_7)^+.\n\n
LOCATION:MR13
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