Finiteness results concerning algebraic power series

Authors :: Julie Decaup
Guillaume Rond
Fuensanta Aroca
Instituto de Matematicas (UNAM)
Universidad Nacional Autónoma de México (UNAM)
Source :: Journal of Pure and Applied Algebra, Journal of Pure and Applied Algebra, Elsevier, 2021, 225 (6), pp.106627. ⟨10.1016/j.jpaa.2020.106627⟩
Publication Year :: 2020
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.<br />12 pages

Language :: English
ISSN :: 00224049
Database :: OpenAIRE
Journal :: Journal of Pure and Applied Algebra, Journal of Pure and Applied Algebra, Elsevier, 2021, 225 (6), pp.106627. ⟨10.1016/j.jpaa.2020.106627⟩
Accession number :: edsair.doi.dedup.....67c8612077a9cbe23a02a27bb0ba7177
Full Text :: https://doi.org/10.1016/j.jpaa.2020.106627⟩