Article Dans Une Revue Journal of the American Mathematical Society Année : 2025

Galois representations modulo $p$ that do not lift modulo $p^2$

Résumé

For every finite group H H and every finite H H -module A A , we determine the subgroup of negligible classes in H 2 ( H , A ) 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 p , every integer n ≥ 3 n\geq 3 , and every field F F containing a primitive p p -th root of unity, there exists a continuous n n -dimensional mod p p representation of the absolute Galois group of F ( x 1 , … , x p ) F(x_1,\dots ,x_p) which does not lift modulo p 2 p^2 . This answers a question of Khare and Serre, and disproves a conjecture of Florence.

Dates et versions

hal-05373722 , version 1 (19-11-2025)

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Citer

Alexander Merkurjev, Federico Scavia. Galois representations modulo $p$ that do not lift modulo $p^2$. Journal of the American Mathematical Society, 2025, 39 (1), pp.73-94. ⟨10.1090/jams/1059⟩. ⟨hal-05373722⟩
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