## Topological Noetherianity of polynomial functors

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Jan Draisma
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**32**(2019), 691-707 Request permission

## 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.## References

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## Additional Information

**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
- MR Author ID: 683807
- ORCID: 0000-0001-7248-8250
- Email: jan.draisma@math.unibe.ch
- 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*. - © Copyright 2019 American Mathematical Society
- Journal: J. Amer. Math. Soc.
**32**(2019), 691-707 - MSC (2010): Primary 13A50, 13A05
- DOI: https://doi.org/10.1090/jams/923
- MathSciNet review: 3981986