The algebraic closure of the power series field in positive characteristic
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- by Kiran S. Kedlaya
- Proc. Amer. Math. Soc. 129 (2001), 3461-3470
- DOI: https://doi.org/10.1090/S0002-9939-01-06001-4
- Published electronically: April 24, 2001
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Abstract:
For $K$ an algebraically closed field, let $K((t))$ denote the quotient field of the power series ring over $K$. The “Newton-Puiseux theorem” states that if $K$ has characteristic 0, the algebraic closure of $K((t))$ is the union of the fields $K((t^{1/n}))$ over $n \in \mathbb {N}$. We answer a question of Abhyankar by constructing an algebraic closure of $K((t))$ for any field $K$ of positive characteristic explicitly in terms of certain generalized power series.References
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Bibliographic Information
- Kiran S. Kedlaya
- Affiliation: Department of Mathematics (Room 2-251), Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, Massachusetts 02139
- Address at time of publication: Department of Mathematics, 970 Evans Hall, University of California, Berkeley, California 94720
- MR Author ID: 349028
- ORCID: 0000-0001-8700-8758
- Email: kedlaya@math.mit.edu, Kedlaya@math.berkeley.edu
- Received by editor(s): November 12, 1998
- Received by editor(s) in revised form: April 15, 2000
- Published electronically: April 24, 2001
- Communicated by: Wolmer V. Vasconcelos
- © Copyright 2001 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 129 (2001), 3461-3470
- MSC (1991): Primary 13F25; Secondary 13J05, 12J25
- DOI: https://doi.org/10.1090/S0002-9939-01-06001-4
- MathSciNet review: 1860477