Abstract
We prove an analogue of the Weierstrass preparation theorem for henselian pairs, generalizing the local case recently proved by Bouthier and Česnavičius. As an application, we construct a henselian analogue of the resultant of p-adic series defined by Berger.
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Acknowledgments
The author is grateful to Henri Lombardi and Herwig Hauser for pointing out references, and to the referee for their remarks.
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Respectfully dedicated to Moshe Jarden
The author was partially supported by the Centre Henri Lebesgue (program ANR-11-LABX-0020-0) and the Geolie project (ANR-15-CE 40-0012).
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Moret-Bailly, L. A henselian preparation theorem. Isr. J. Math. 257, 519–531 (2023). https://doi.org/10.1007/s11856-023-2545-1
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DOI: https://doi.org/10.1007/s11856-023-2545-1