Open Access
2015 Classifying extensions of the field of formal Laurent series over $\mathbb{F}_p$
Jim Brown, Alfeen Hasmani, Lindsey Hiltner, Angela Kraft, Daniel Scofield, Kirsti Wash
Rocky Mountain J. Math. 45(1): 115-130 (2015). DOI: 10.1216/RMJ-2015-45-1-115


In previous works, Jones and Roberts and Pauli and Roblot have studied finite extensions of the $p$-adic numbers $\mathbb{Q}_p$. This paper focuses on results for local fields of characteristic~$p$. In particular, we are able to produce analogous results to Jones and Roberts in the case that the characteristic does not divide the degree of the field extension. Also, in this case, following from the work of Pauli and Roblot, we prove that the defining polynomials of these extensions can be written in a simple form amenable to computation. Finally, if $p$ is the degree of the extension, we show there are infinitely many extensions of this degree and thus these cannot be classified in the same manner.


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Jim Brown. Alfeen Hasmani. Lindsey Hiltner. Angela Kraft. Daniel Scofield. Kirsti Wash. "Classifying extensions of the field of formal Laurent series over $\mathbb{F}_p$." Rocky Mountain J. Math. 45 (1) 115 - 130, 2015.


Published: 2015
First available in Project Euclid: 7 April 2015

zbMATH: 1320.11110
MathSciNet: MR3334205
Digital Object Identifier: 10.1216/RMJ-2015-45-1-115

Primary: 11S15
Secondary: 11S05

Rights: Copyright © 2015 Rocky Mountain Mathematics Consortium

Vol.45 • No. 1 • 2015
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