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Journal of the American Mathematical Society

Published by the American Mathematical Society, the Journal of the American Mathematical Society (JAMS) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6834 (online) ISSN 0894-0347 (print)

The 2020 MCQ for Journal of the American Mathematical Society is 4.79.

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Topological Noetherianity of polynomial functors
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by Jan Draisma HTML | PDF
J. Amer. Math. Soc. 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.
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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