Differential characters of abelian varieties over \(p\)-adic fields
type: Item
instance of: scholarly article
title: Differential characters of abelian varieties over \(p\)-adic fields
zbMATH Open document ID: 0841.14037
DOI: 10.1007/BF01231447
published in: Inventiones Mathematicae
publication date: 1996-05-19T00:00:00Z
full work available at URL: https://eudml.org/doc/144323
review text: 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)].
Mathematics Subject Classification ID: 14K15
Mathematics Subject Classification ID: 13N05
Mathematics Subject Classification ID: 14G20
zbMATH DE Number: 861966
zbMATH Keywords: \(p\)-adic fields
zbMATH Keywords: differential character
zbMATH Keywords: abelian scheme
zbMATH Keywords: theorem of the kernel
zbMATH Keywords: arithmetic jet theory
author: Alexandru Buium
reviewed by: Alexandru Buium
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 861966