The algebraic closure of the power series field in positive characteristic

Author:
Kiran S. Kedlaya

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

Published electronically:
April 24, 2001

MathSciNet review:
1860477

Full-text PDF

Abstract | References | Similar Articles | Additional Information

For an algebraically closed field, let denote the quotient field of the power series ring over . The ``Newton-Puiseux theorem'' states that if has characteristic 0, the algebraic closure of is the union of the fields over . We answer a question of Abhyankar by constructing an algebraic closure of for any field of positive characteristic explicitly in terms of certain generalized power series.

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Additional 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

Email:
kedlaya@math.mit.edu, Kedlaya@math.berkeley.edu

DOI:
https://doi.org/10.1090/S0002-9939-01-06001-4

Keywords:
Power series,
generalized power series,
algebraic closure,
Puiseux expansions,
Mal'cev-Neumann rings

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

Article copyright:
© Copyright 2001
American Mathematical Society