Kedlaya, Kiran S. Power series and \(p\)-adic algebraic closures. (English) Zbl 0980.12002 J. Number Theory 89, No. 2, 324-339 (2001). Let \(K\) be an algebraically closed field of characteristic \(p>0\), \(W(K)\) the corresponding Witt ring. The author gives an explicit description of the \(p\)-adic completion of the integral closure \(\overline{W(K)}\) of \(W(K)\) in an algebraic closure of its fraction field. The construction uses generalized power series introduced by B. Poonen [Enseign. Math., II. Sér. 39, 87-106 (1993; Zbl 0807.12006)], and the description of the algebraic closure of a field of power series given by the author [K. S. Kedlaya, Proc. Am. Math. Soc. 129, 3461-3470 (2001; Zbl 1012.12007)]. The basic step of an independent interest is a construction of a surjection of \(W(K[[t]])\) onto the \(p\)-adic closure of \(\overline{W(K)}\). Reviewer: Anatoly N.Kochubei (Kyïv) Cited in 11 Documents MSC: 12J25 Non-Archimedean valued fields 11S85 Other nonanalytic theory Keywords:Witt ring; algebraic closure; generalized power series Citations:Zbl 0807.12006; Zbl 1012.12007 × Cite Format Result Cite Review PDF Full Text: DOI arXiv References: [1] Fontaine, J. M.; Wintenberger, J. P., Le “corps de normes” de certaines extensions algébriques de corps locaux, C. R. Acad. Sci. Paris Sér. I Math., 288, 367-370 (1979) · Zbl 0475.12020 [2] Hahn, H., Über die nichtarchimedische Größensysteme, Gesammelte Abhandlungen I (1995), Springer-Verlag: Springer-Verlag Berlin/New York [3] Kaplansky, I., Maximal fields with valuations, Duke Math J., 9, 303-321 (1942) · Zbl 0063.03135 [4] K. S. Kedlaya, The algebraic closure of the power series field in positive characteristic, in, Proc. Amer. Math. Soc, in press; also available as xxx preprint math.AG/9810142.; K. S. Kedlaya, The algebraic closure of the power series field in positive characteristic, in, Proc. Amer. Math. Soc, in press; also available as xxx preprint math.AG/9810142. [5] Krull, W., Allgemeine Bewertungstheorie, J. Math., 167, 160-196 (1932) · JFM 58.0148.02 [6] Lampert, D., Algebraic \(p\)-adic expansions, J. Number Theory, 23, 279-284 (1986) · Zbl 0586.12021 [7] Poonen, B., Maximally complete fields, Enseign. Math., 39, 87-106 (1993) · Zbl 0807.12006 [8] Ribenboim, P., Fields: algebraically closed and others, Manuscripta Math., 75, 115-150 (1992) · Zbl 0767.12001 [9] Serre, J.-P., Local Fields (1979), Springer-Verlag: Springer-Verlag Berlin/New York · Zbl 0423.12016 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.