论文标题
用Frobenius-Proxtive结构对代数曲线进行量化
Quantization on Algebraic Curves with Frobenius-Projective Structure
论文作者
论文摘要
在本文中，我们研究了在阳性特征中代数曲线上定义的变形量化与frobenius-prokoxtive结构之间的关系。 frobenius-progentive结构是Y. Hoshi引入的Riemann表面上复杂的投影结构的类似物。这样的附加结构具有一些等效的对象，例如，休眠的$ \ mathrm {pgl} _2 $ - oper和一个具有完整解决方案的投射连接。本文的主要结果通过Frobenius-Projective结构在代数曲线上的零截面减去零截面上的Frobenius-Contant量化的规范结构。它可以认为是D. Ben-Zvi和I. Biswas对结果的积极特征类似物。最后，我们给出了该结果的较高维度，如I. Biswas在复杂情况下所证明的那样。
In the present paper, we study the relationship between deformation quantizations and Frobenius-projective structures defined on an algebraic curve in positive characteristic. A Frobenius-projective structure is an analogue of a complex projective structure on a Riemann surface, which was introduced by Y. Hoshi. Such an additional structure has some equivalent objects, e.g., a dormant $\mathrm{PGL}_2$-oper and a projective connection having a full set of solutions. The main result of the present paper provides a canonical construction of a Frobenius-constant quantization on the cotangent space minus the zero section on an algebraic curve by means of a Frobenius-projective structure. It may be thought of as a positive characteristic analogue of a result by D. Ben-Zvi and I. Biswas. Finally, we give a higher-dimensional variant of this result, as proved by I. Biswas in the complex case.
