On de Jong's conjecture
| dc.creator | Gaitsgory, Dennis | |
| dc.date | 2004-02-11 | |
| dc.date | 2006-04-01 | |
| dc.date.accessioned | 2026-07-07T06:35:59Z | |
| dc.date.available | 2026-07-07T06:35:59Z | |
| dc.description | Let $X$ be a smooth projective curve over a finite field $F_q$. Let $ρ$ be a continuous representation $π(X)\to GL_n(F)$, where $F=F_l((t))$ with $F_l$ being another finite field of order prime to $q$. Assume that $ρ|_{π(\bar{X})}$ is irreducible. De Jong's conjecture says that in this case $ρ(π(\bar{X}))$ is finite. As was shown in the original paper of de Jong, this conjecture follows from an existence of an $F$-valued automorphic form corresponding to $ρ$ is the sense of Langlands. The latter follows, in turn, from a version of the Geometric Langlands conjecture. In this paper we sketch a proof of the required version of the geometric conjecture, assuming that $char(F)\neq 2$, thereby proving de Jong's conjecture in this case. | |
| dc.identifier | https://arxiv.org/abs/math/0402184 | |
| dc.identifier | http://arxiv.org/abs/math/0402184 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/99955 | |
| dc.subject | Algebraic Geometry | |
| dc.title | On de Jong's conjecture | |
| dc.type | text |