Topological Noetherianity of polynomial functors

Draisma, Jan¹

¹ Mathematisches Institut, Universität Bern, Sidlerstrasse 5, 3012 Bern; and Eindhoven University of Technology, P.O. Box 513, 5600 MB, Eindhoven, The Netherlands

Journal of the American Mathematical Society, Tome 32 (2019) no. 3, pp. 691-707

Résumé

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.

Détail

DOI : 10.1090/jams/923

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