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arXiv · 2009.05084

The relatively perfect Greenberg transform and cycle class maps

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 N\'eron 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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Alessandra Bertapelle, Takashi Suzuki. 2020-09-10. The relatively perfect Greenberg transform and cycle class maps. https://doi.org/10.1007/s00229-024-01576-w

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