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SUMMARY:Federico Scavia (Université Sorbonne Paris Nord)
DTSTART:20251022T150000Z
DTEND:20251022T160000Z
DTSTAMP:20260418T065700Z
UID:LNTS/172
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/LNTS/172/">T
 he lifting problem for Galois representations</a>\nby Federico Scavia (Uni
 versité Sorbonne Paris Nord) as part of London number theory seminar\n\nL
 ecture held in Imperial College London\, Room 139.\n\nAbstract\nFor every 
 finite group H and every finite H-module A\, we determine the subgroup of 
 negligible classes in H^2(H\, A)\, in the sense of Serre\, over fields wit
 h enough roots of unity. As a consequence\, we show that for every odd pri
 me p and every field F containing a primitive p-th root of unity\, there e
 xists a continuous 3-dimensional mod p representation of the absolute Galo
 is group of F(x_1\, ...\, x_p) which does not lift modulo p^2. We also con
 struct continuous 5-dimensional Galois representations mod 2 which do not 
 lift modulo 4. This answers a question of Khare and Serre\, and disproves 
 a conjecture of Florence. This is joint work with Alexander Merkurjev.\n
LOCATION:https://researchseminars.org/talk/LNTS/172/
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