论文标题
算术PDE设置中的算术差异几何形状，I：连接
Arithmetic differential geometry in the arithmetic PDE setting, I: connections
论文作者
论文摘要
这是有关论文开发算术PDE类似物的系列中的第一个。 Fermat商操作在Absoute Galois组的几个Frobenius元素方面发挥了部分衍生物的作用。在这种情况下证明了地球学以及Levi-Civita和Chern连接的存在和独特性。在本文的续集中，将开发出算术理论和特征性类别的理论。
This is the first in a series on papers developing an arithmetic PDE analogue of Riemannian geometry. The role of partial derivatives is played by Fermat quotient operations with respect to several Frobenius elements in the absolute Galois group of a $p$-adic field. Existence and uniqueness of geodesics and of Levi-Civita and Chern connections are proved in this context. In a sequel to this paper a theory of arithmetic Riemannian curvature and characteristic classes will be developed.
