Differential characters of abelian varieties over \(p\)-adic fields
For a given complete discrete valuation ring \(R\) in mixed characteristic and each choice of a local parameter \(\pi\) one defines an analogue of ``derivation with respect to \(\pi\)'', \(\delta : R \to R\) depending on \(\pi\). Then for every abelian scheme \(A\) over \(R\) a notion of ``differential character'' \(A(R) \to R\) with respect to \(\delta\) is defined. The main result of the paper say that the intersection of the kernels of all differential characters is ``small''. This should be viewed as an arithmetic analogue of the theorem of the kernel [\textit{Yu. I. Manin}, Am. Math. Soc., Transl., II. Ser. 37, 59-78 (1964); translation from Izv. Akad. Nauk SSSR, Ser. Mat. 22, 737-756 (1958; Zbl 0151.27503)] and \textit{C. Chai} [Am. J. Math. 113, No. 3, 387-389 (1991; Zbl 0759.14017)]. As a main tool an arithmetic jet theory is developed in analogy with the function field case treated by the author [Ann. Math., II. Ser. 136, No. 3, 557-567 (1992; Zbl 0817.14021)].
scientific article; zbMATH DE number 861966
scientific article