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2018•Proceedings of the London Mathematical SocietyOpen access

Support of Laurent series algebraic over the field of formal power series

Fuensanta Aroca, Guillaume Rond

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Abstract

This work is devoted to the study of the support of a Laurent series in several variables which is algebraic over the ring of power series over a characteristic zero field. Our first result is the existence of a kind of maximal dual cone of the support of such a Laurent series. As an application of this result we provide a gap theorem for Laurent series which are algebraic over the field of formal power series. We also relate these results to Diophantine properties of the fields of Laurent series.

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This work is devoted to the study of the support of a Laurent series in several variables which is algebraic over the ring of power series over a characteristic zero field. Our first result is the existence of a kind of maximal dual cone of the support of such a Laurent series. As an application of this result we provide a gap theorem for Laurent series which are algebraic over the field of formal power series. We also relate these results to Diophantine properties of the fields of Laurent series.

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Available abstract

This work is devoted to the study of the support of a Laurent series in several variables which is algebraic over the ring of power series over a characteristic zero field. Our first result is the existence of a kind of maximal dual cone of the support of such a Laurent series. As an application of this result we provide a gap theorem for Laurent series which are algebraic over the field of formal power series. We also relate these results to Diophantine properties of the fields of Laurent series.

Key concepts: Laurent series, Formal power series, Mathematics, Power series, Series (stratigraphy), Algebraic number, Field (mathematics), Laurent polynomial

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