Kloosterman联络的Hodge理论
代数几何
2022-06-14 v5 数论
摘要
我们构造了与Kloosterman和对称幂矩相关的有理数上的动机，并证明它们的L函数可亚纯延拓到复平面，且满足Broadhurst和Roberts所猜想的函数方程。尽管所讨论的动机结果证明是“经典的”，我们仍通过其在指数混合Hodge结构实现上的非正则Hodge filtration来计算它们的Hodge数。我们证明所有Hodge数要么为零要么为一，这得益于Patrikis和Taylor近期的结果，意味着潜在自守性。
引用
@article{arxiv.1810.06454,
title = {Hodge theory of Kloosterman connections},
author = {Javier Fresán and Claude Sabbah and Jeng-Daw Yu},
journal= {arXiv preprint arXiv:1810.06454},
year = {2022}
}
备注
v2: Results and exposition improved. v3: Substantial revision after referee reports. The main construction now takes place in the setting of exponential mixed Hodge structures. We partially reorganized the material and removed one of the appendices. Some statements have been strengthened, several proofs simplified, and a few mistakes corrected. v5: Final published version