On the geometric Langlands conjecture
代数几何
2007-05-23 v3
摘要
Let X be a smooth, complete, geometrically connected curve over a field of characteristic p. The geometric Langlands conjecture states that to each irreducible rank n local system E on X one can attach a perverse sheaf on the moduli stack of rank n bundles on X (irreducible on each connected component), which is a Hecke eigensheaf with respect to E. In this paper we derive the geometric Langlands conjecture from a certain vanishing conjecture. Furthermore, using recent results of Lafforgue, we prove this vanishing conjecture, and hence the geometric Langlands conjecture, in the case when the ground field is finite.
引用
@article{arxiv.math/0012255,
title = {On the geometric Langlands conjecture},
author = {E. Frenkel and D. Gaitsgory and K. Vilonen},
journal= {arXiv preprint arXiv:math/0012255},
year = {2007}
}