Analytic Ax-Kochen-Ersov theory with lifts of the residue field and value group
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- by Neer Bhardwaj and Lou van den Dries;
- Trans. Amer. Math. Soc. Ser. B 11 (2024), 1015-1064
- DOI: https://doi.org/10.1090/btran/198
- Published electronically: July 26, 2024
- HTML | PDF
Abstract:
We develop an extension theory for analytic valuation rings in order to establish Ax-Kochen-Ersov (AKE) type results for these structures. New is that we can add in salient cases lifts of the residue field and the value group and show that the induced structure on the lifted residue field is just its field structure, and on the lifted value group is just its ordered abelian group structure. This restores an analogy with the nonanalytic AKE-setting that was missing in earlier treatments of analytic AKE-theory.References
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Bibliographic Information
- Neer Bhardwaj
- Affiliation: Department of Mathematics, Weizmann Institute of Science, Rehovot, Israel
- MR Author ID: 1483229
- ORCID: 0000-0003-0932-2391
- Email: nbhardwaj@msri.org
- Lou van den Dries
- Affiliation: Department of Mathematics, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801
- MR Author ID: 59845
- Email: vddries@illinois.edu
- Received by editor(s): January 9, 2024
- Received by editor(s) in revised form: April 25, 2024
- Published electronically: July 26, 2024
- © Copyright 2024 by the authors under Creative Commons Attribution-NonCommercial 3.0 License (CC BY NC 3.0)
- Journal: Trans. Amer. Math. Soc. Ser. B 11 (2024), 1015-1064
- MSC (2020): Primary 03C10, 32B05; Secondary 03C60, 12J25, 13J15, 13L05
- DOI: https://doi.org/10.1090/btran/198
- MathSciNet review: 4778625