Finiteness results concerning algebraic power series

2020/02/19 by Aroca, Fuensanta, Decaup, Julie, Rond, Guillaume
#Algebraic Geometry (math.AG) #Commutative Algebra (math.AC) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2002.08452

Abstract

We construct an explicit filtration of the ring of algebraic power series by finite dimensional constructible sets, measuring the complexity of these series. As an application, we give a bound on the dimension of the set of algebraic power series of bounded complexity lying on an algebraic variety defined over the field of power series.

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