Quantization on algebraic curves with Frobenius-projective structure
Quantization on algebraic curves with Frobenius-projective structure
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具有 Frobenius 射影结构的代数曲线的量化
DOI：
10.1007/s11005-022-01550-1
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发表时间：
2022
期刊：
影响因子：
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通讯作者：
Yasuhiro Wakabayashi
中科院分区：
文献类型：
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作者：
Endo Naoki;Goto Shiro;Isobe Ryotaro;Ryotaro Isobe;Ryotaro Isobe;Ryotaro Isobe;Ryotaro Isobe;Henrik Bachmann;Henrik Bachmann;Henrik Bachmann;Henrik Bachmann;Masaru Nagaoka;Masaru Nagaoka;Masaru Nagaoka;Masaru Nagaoka;Masaru Nagaoka;鈴木雄太;Yasuhiro Wakabayashi;Yasuhiro Wakabayashi
本文研究了在正特征代数曲线上定义的变形量化与frobenius -射影结构之间的关系。frobenius射影结构是由Y. Hoshi提出的黎曼曲面上复杂射影结构的类似物。这种附加结构具有一些等价对象，例如，具有全套解的休眠节点和投影连接。本文的主要结果利用frobenius -射影结构给出了在代数曲线上的余切空间负零截面上的frobenius常数量子化的标准构造。它可以被认为是D. Ben-Zvi和I. Biswas的结果的正特征类比。最后，该结果推广到高维变量，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-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, this result generalizes to higher-dimensional varieties, as proved by I. Biswas in the complex case.