The lifting problem for Galois representations

Abstract: For 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 with enough roots of unity. As a consequence, we show that for every odd prime p and every field F containing a primitive p-th root of unity, there exists a continuous 3-dimensional mod p representation of the absolute Galois group of F(x_1, ..., x_p) which does not lift modulo p^2. We also construct 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.

number theory

Audience: researchers in the topic

London number theory seminar

Series comments: For reminders, join the (very low traffic) mailing list at mailman.ic.ac.uk/mailman/listinfo/london-number-theory-seminar

For a record of talks predating this website see: wwwf.imperial.ac.uk/~buzzard/LNTS/numbtheo_past.html