The Greenberg functor revisited
Number Theory
2022-02-22 v6 Algebraic Geometry
Abstract
The proof, but not the statement, of Proposition 18.2 contained an error which is repaired in this version. See Remark 18.3 in this version. No other changes. We extend Greenberg's original construction to arbitrary (in particular, non-reduced) schemes over (certain types of) local artinian rings. We then establish a number of basic properties of the extended functor and determine, for example, its behavior under Weil restriction. We also discuss a formal analog of the functor.
Keywords
Cite
@article{arxiv.1311.0051,
title = {The Greenberg functor revisited},
author = {Alessandra Bertapelle and Cristian D. Gonzalez-Aviles},
journal= {arXiv preprint arXiv:1311.0051},
year = {2022}
}
Comments
120 pages. The proof, but not the statement, of Proposition 18.2 contained an error which is repaired in this version. See the new Remark 18.3. No other changes