Topological noetherianity for powers of algebraic representations
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arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866910106736656384 |
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| author | Danelon, Alessandro |
| author_facet | Danelon, Alessandro |
| contents | Powers of a polynomial $\operatorname{GL}$-representation are topologically Noetherian under the action of $\operatorname{Sym} \times \operatorname{GL}$. We extend this result to powers of algebraic representations of the orthogonal and the symplectic groups, proving topological Noetherianity under the action of $\operatorname{Sym} \times \operatorname{O}$ and $\operatorname{Sym} \times \operatorname{Sp}$ respectively. This work builds on arXiv:2212.05790 and arXiv:1708.06420, and it provides further evidence that infinite powers of topologically Noetherian varieties remain topologically Noetherian up to permutations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_23186 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Topological noetherianity for powers of algebraic representations Danelon, Alessandro Representation Theory Commutative Algebra Algebraic Geometry Powers of a polynomial $\operatorname{GL}$-representation are topologically Noetherian under the action of $\operatorname{Sym} \times \operatorname{GL}$. We extend this result to powers of algebraic representations of the orthogonal and the symplectic groups, proving topological Noetherianity under the action of $\operatorname{Sym} \times \operatorname{O}$ and $\operatorname{Sym} \times \operatorname{Sp}$ respectively. This work builds on arXiv:2212.05790 and arXiv:1708.06420, and it provides further evidence that infinite powers of topologically Noetherian varieties remain topologically Noetherian up to permutations. |
| title | Topological noetherianity for powers of algebraic representations |
| topic | Representation Theory Commutative Algebra Algebraic Geometry |
| url | https://arxiv.org/abs/2601.23186 |