正特征下的受限几何Langlands等价
The Restricted Geometric Langlands Equivalence in Positive Characteristic
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具体内容
稿件研究正特征p（ℓ≠p）下光滑射影连通曲线与连通约化群上的受限几何Langlands等价，作者声称在两类情形中证明了该等价的Q̄ℓ线性版本：在F̄q上假设受限理论的四个特征条件；在任意代数闭域上还要求p为非常好的素数且不整除Weyl群阶。摘要表示这在此范围内证明了Gaitsgory–Raskin的全支撑猜想。该结果若成立，将推进几何Langlands纲领在正特征下的受限形式。
- 研究对象为正特征光滑射影曲线与连通约化群的受限几何Langlands等价。
- 在F̄q上需假设受限理论的四个特征条件，任意代数闭域另加p非常好且不整除Weyl群阶。
- 作者声称由此证明Gaitsgory–Raskin全支撑猜想的相关情形。
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英文原始摘要
We prove the $`\overline{\mathbb Q}_\ell`$-linear restricted geometric Langlands equivalence for smooth projective connected curves and connected reductive groups in characteristic p > 0, with ℓ ≠ p, in two regimes. Over $`\overline{\mathbb F}_q`$, we assume the four characteristic conditions of the restricted theory stated below. Over arbitrary algebraically closed fields, we assume these conditions and additionally that p is very good and does not divide the Weyl-group order. This proves Gaitsgory–Raskin's full-support conjecture [[12, Conjecture 1.3.10]](https://arxiv.org/abs/2508.02237v1) in these regimes.
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