Topological Noetherianity of polynomial functors

Draisma, Jan

doi:10.1090/jams/923

Topological Noetherianity of polynomial functors
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by Jan Draisma

J. Amer. Math. Soc. 32 (2019), 691-707

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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