Mod $\ell$ representations of arithmetic fundamental groups II (A conjecture of A.J. de Jong)
| dc.creator | Boeckle, Gebhard | |
| dc.creator | Khare, Chandrashekhar | |
| dc.date | 2003-12-29 | |
| dc.date | 2004-04-17 | |
| dc.date.accessioned | 2026-07-07T05:04:15Z | |
| dc.date.available | 2026-07-07T05:04:15Z | |
| dc.description | As a sequel to our proof of the analog of Serre's conjecture for function fields in Part I of this work, we study in this paper the deformation rings of $n$-dimensional mod $\ell$ representations $ρ$ of the arithmetic fundamental group $π_1(X)$ where $X$ is a geometrically irreducible, smooth curve over a finite field $k$ of characteristic $p$ ($\neq \ell$). We are able to show in many cases that the resulting rings are finite flat over $\BZ_\ell$. The proof principally uses a lifting result of the authors in Part I of this two-part work, Taylor-Wiles systems and the result of Lafforgue. This implies a conjecture of A.J. ~de Jong for representations with coefficients in power series rings over finite fields of characteristic $\ell$, that have this mod $\ell$ representation as their reduction. | |
| dc.description | This revised version is cleaner, although not substantially different. We check that our arguments work for \ell=2 | |
| dc.identifier | https://arxiv.org/abs/math/0312490 | |
| dc.identifier | http://arxiv.org/abs/math/0312490 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/69732 | |
| dc.subject | Number Theory | |
| dc.subject | Algebraic Geometry | |
| dc.title | Mod $\ell$ representations of arithmetic fundamental groups II (A conjecture of A.J. de Jong) | |
| dc.type | text |