The relatively perfect Greenberg transform and cycle class maps

Pub Date : 2024-06-17 DOI:10.1007/s00229-024-01576-w
Alessandra Bertapelle, Takashi Suzuki
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Abstract

Given a scheme over a complete discrete valuation ring of mixed characteristic with perfect residue field, the Greenberg transform produces a new scheme over the residue field thicker than the special fiber. In this paper, we will generalize this transform to the case of imperfect residue field. We will then construct a certain kind of cycle class map defined on this generalized Greenberg transform applied to the Néron model of a semi-abelian variety, which takes values in the relatively perfect nearby cycle functor defined by Kato and the second author.

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相对完美的格林伯格变换和循环类图
给定一个在具有完美残差域的混合特征的完整离散估值环上的方案,格林伯格变换会在比特殊纤维更厚的残差域上产生一个新方案。在本文中,我们将把这种变换推广到不完全残差域的情况。然后,我们将构造一种定义在这种广义格林伯格变换上的循环类映射,它应用于半阿贝尔变种的内龙模型,在加藤和第二作者定义的相对完美邻近循环函子中取值。
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