Power series and p-adic algebraic closures

1999/06/04 by Kiran S. Kedlaya, Kedlaya, Kiran S. · 1 citation
Mathematics · #12F05 (Primary) 14Q05 (Secondary) #Advanced Algebra and Geometry #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Commutative Algebra (math.AC) #FOS: Mathematics #Rings and Algebras (math.RA) #math.AC #math.AG #math.RA #msc:12F05 #msc:14Q05

paper · pdf · doi:10.48550/arxiv.math/9906030

12 pages; uses AMSLaTeX and xypic for one figure (replaced 16 Dec 1999: corrected proof of Theorem 1)

openalex publication_date 1999/06/04 · arxiv created 1999/12/16 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In an earlier preprint (math.AG/9810142) we gave an explicit description of the algebraic closure of the field of power series over a field of characteristic p, in terms of "generalized power series". In this paper, we give an analogous description of the algebraic closure of the fraction field of the Witt ring of a field of characteristic p, using an analogue of generalized power series in mixed characteristic due to Poonen.

Cited by

• On the p-adic transcendence of ∑_k=1^∞ p^-1/pk

Related

• The Algebraic Closure of the Power Series Field in Positive Characteristic
• On the algebraicity of generalized power series
• About the algebraic closure of formal power series in several variables
• Algebraic elements over the ring of power series
• The Weierstrass preparation theorem and resultants of p-adic power series