The aim of this article is to give a self-contained account of the algebra and model theory of Cohen rings, a natural generalization of Witt rings. Witt rings are only valuation rings in case the residue field is perfect, and Cohen rings arise as the Witt ring analogon over imperfect residue fields. Just as one studies truncated Witt rings to understand Witt rings, we study Cohen rings of positive characteristic as well as of characteristic zero. Our main results are a relative completeness and a relative model completeness result for Cohen rings, which imply the corresponding Ax-Kochen/Ershov type results for unramified henselian valued fields also in case the residue field is imperfect.
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Mots clés : model theory, henselian valued fields, Cohen rings, Ax-Kochen-Ershov
Sylvy Anscombe 1 ; Franziska Jahnke 2
CC-BY-NC-ND 4.0
@article{CML_2022__14_2_1_0,
author = {Sylvy Anscombe and Franziska Jahnke},
title = {The model theory of {Cohen} rings},
journal = {Confluentes Mathematici},
pages = {1--28},
publisher = {Institut Camille Jordan},
volume = {14},
number = {2},
year = {2022},
doi = {10.5802/cml.84},
language = {en},
url = {https://cml.centre-mersenne.org/articles/10.5802/cml.84/}
}
TY - JOUR AU - Sylvy Anscombe AU - Franziska Jahnke TI - The model theory of Cohen rings JO - Confluentes Mathematici PY - 2022 SP - 1 EP - 28 VL - 14 IS - 2 PB - Institut Camille Jordan UR - https://cml.centre-mersenne.org/articles/10.5802/cml.84/ DO - 10.5802/cml.84 LA - en ID - CML_2022__14_2_1_0 ER -
Sylvy Anscombe; Franziska Jahnke. The model theory of Cohen rings. Confluentes Mathematici, Tome 14 (2022) no. 2, pp. 1-28. doi : 10.5802/cml.84. https://cml.centre-mersenne.org/articles/10.5802/cml.84/
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