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Topological Noetherianity of polynomial functors


Author: Jan Draisma
Journal: J. Amer. Math. Soc. 32 (2019), 691-707
MSC (2010): Primary 13E05, 14M12, 15A69, 20G05
DOI: https://doi.org/10.1090/jams/923
Published electronically: April 18, 2019
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Abstract: We prove that any finite-degree polynomial functor over an infinite field is topologically Noetherian. This theorem is motivated by the recent resolution, by Ananyan-Hochster, of Stillman's conjecture; and a recent Noetherianity proof by Derksen-Eggermont-Snowden for the space of cubics. Via work by Erman-Sam-Snowden, our theorem implies Stillman's conjecture and indeed boundedness of a wider class of invariants of ideals in polynomial rings with a fixed number of generators of prescribed degrees.


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Jan Draisma
Affiliation: Mathematisches Institut, Universität Bern, Sidlerstrasse 5, 3012 Bern; and Eindhoven University of Technology, P.O. Box 513, 5600 MB, Eindhoven, The Netherlands
Email: jan.draisma@math.unibe.ch

DOI: https://doi.org/10.1090/jams/923
Received by editor(s): May 11, 2017
Received by editor(s) in revised form: January 10, 2019
Published electronically: April 18, 2019
Additional Notes: The author was partially supported by the NWO Vici grant entitled Stabilisation in Algebra and Geometry.
Article copyright: © Copyright 2019 American Mathematical Society