中文

混合延拓的Tannakian基本群

代数几何 2024-07-18 v2 数论

摘要

A1,A2,A3A_1, A_2, A_3 为特征为零的域上的中性Tannakian范畴中半单态对象。设 LLA2A_2 关于 A1A_1 的延拓,NNA3A_3 关于 A2A_2 的延拓。设 MMNN 关于 LL 的混合延拓(extension panaché)。在非常温和且自然的假设下,我们研究 MM 的Tannakian基本群的单边解。我们的结果适用的例子包括任意三个权重混合动力学的动力学Galois群的单边解。作为应用,我们给出了在任何动力学范畴中1-动力学单边解的证明(其中 Ext1(1,Q(1))Ext^1(1,\mathbb{Q}(1)) 的结构正如预期),该结果在André的Norims范畴中亦成立。

关键词

引用

@article{arxiv.2407.01379,
  title  = {Tannakian fundamental groups of blended extensions},
  author = {Payman Eskandari},
  journal= {arXiv preprint arXiv:2407.01379},
  year   = {2024}
}

备注

Comments are welcome! Changes to the first version: Changes have been made to weaken the hypotheses. An argument has been added to show an isomorphism is independent of the choice of the fiber functor. Some typos have been fixed and other minor changes have been made to improve the exposition