Topological noetherianity of polynomial functors

Jan Draisma (Corresponding author)

Research output: Contribution to journalArticleAcademicpeer-review

2 Citations (Scopus)
3 Downloads (Pure)

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.

Original languageEnglish
Pages (from-to)691-707
Number of pages17
JournalJournal of the American Mathematical Society
Volume32
Issue number3
DOIs
Publication statusPublished - 18 Apr 2019

Fingerprint

Functor
Polynomials
Polynomial
Noetherian
Polynomial ring
Theorem
Boundedness
Generator
Imply
Invariant
Class

Cite this

@article{80a14b6094424f1ba591a4424585b8b9,
title = "Topological noetherianity of polynomial functors",
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.",
author = "Jan Draisma",
year = "2019",
month = "4",
day = "18",
doi = "10.1090/jams/923",
language = "English",
volume = "32",
pages = "691--707",
journal = "Journal of the American Mathematical Society",
issn = "0894-0347",
publisher = "American Mathematical Society",
number = "3",

}

Topological noetherianity of polynomial functors. / Draisma, Jan (Corresponding author).

In: Journal of the American Mathematical Society, Vol. 32, No. 3, 18.04.2019, p. 691-707.

Research output: Contribution to journalArticleAcademicpeer-review

TY - JOUR

T1 - Topological noetherianity of polynomial functors

AU - Draisma, Jan

PY - 2019/4/18

Y1 - 2019/4/18

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85068525531&partnerID=8YFLogxK

U2 - 10.1090/jams/923

DO - 10.1090/jams/923

M3 - Article

AN - SCOPUS:85068525531

VL - 32

SP - 691

EP - 707

JO - Journal of the American Mathematical Society

JF - Journal of the American Mathematical Society

SN - 0894-0347

IS - 3

ER -