Quantization on Algebraic Curves with Frobenius-Projective Structure
Abstract
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, we give a higher-dimensional variant of this result, as proved by I. Biswas in the complex case.
Cite
@article{arxiv.2004.04283,
title = {Quantization on Algebraic Curves with Frobenius-Projective Structure},
author = {Yasuhiro Wakabayashi},
journal= {arXiv preprint arXiv:2004.04283},
year = {2020}
}
Comments
27 pages