Galois representations modulo $p$ that do not lift modulo $p^2$
| Autor: | Merkurjev, Alexander, Scavia, Federico |
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| Rok vydání: | 2024 |
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| Druh dokumentu: | Working Paper |
| Popis: | 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 $p$, every integer $n\geq 3$, and every field $F$ containing a primitive $p$-th root of unity, there exists a continuous $n$-dimensional mod $p$ representation of the absolute Galois group of $F(x_1,\dots,x_p)$ which does not lift modulo $p^2$. This answers a question of Khare and Serre, and disproves a conjecture of Florence. Comment: 21 pages |
| Databáze: | arXiv |
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