Bik, Michel; Danelon, Alessandro; Draisma, Jan (2022). Topological Noetherianity of polynomial functors II: base rings with Noetherian spectrum. Mathematische Annalen, 385(3-4), pp. 1879-1921. Springer 10.1007/s00208-022-02386-9
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In a previous paper, the third author proved that finite-degree polynomial functors over infinite fields are topologically Noetherian. In this paper, we prove that the same holds for polynomial functors from free R-modules to finitely generated R-modules, for any commutative ring R whose spectrum is Noetherian. As Erman–Sam–Snowden pointed out, when applying this with R=Z to direct sums of symmetric powers, one of their proofs of a conjecture by Stillman becomes characteristic-independent. Our paper advertises and further develops the beautiful but not so well-known machinery of polynomial laws. In particular, to any finitely generated R-module M we associate a topological space, which we show is Noetherian when Spec(R)
is; this is the degree-zero case of our result on polynomial functors.
Item Type: |
Journal Article (Original Article) |
|---|---|
Division/Institute: |
08 Faculty of Science > Department of Mathematics and Statistics > Institute of Mathematics |
UniBE Contributor: |
Bik, Michel Arthur, Danelon, Alessandro, Draisma, Jan |
Subjects: |
500 Science > 510 Mathematics |
ISSN: |
0025-5831 |
Publisher: |
Springer |
Language: |
English |
Submitter: |
Zarif Ibragimov |
Date Deposited: |
14 Mar 2023 10:04 |
Last Modified: |
02 Apr 2023 02:14 |
Publisher DOI: |
10.1007/s00208-022-02386-9 |
BORIS DOI: |
10.48350/179982 |
URI: |
https://boris.unibe.ch/id/eprint/179982 |
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