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arXiv · 1703.06219

Cubic Fields: A Primer

Sophie Marques·Kenneth Ward
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Abstract

We classify all cubic extensions of any field of arbitrary characteristic, up to isomorphism, via an explicit construction involving three fundamental types of cubic forms. We deduce a classification of any Galois cubic extension of a field. The splitting and ramification of places in a separable cubic extension of any global function field are completely determined, and precise Riemann-Hurwitz formulae are given. In doing so, we determine the decomposition of any cubic polynomial over a finite field.

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Sophie Marques, Kenneth Ward. 2017-03-18. Cubic Fields: A Primer. https://arxiv.org/abs/1703.06219

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