A base change framework for tensor functions
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| Accesso online: | |
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| _version_ | 1866918381312016384 |
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| author | Chen, Qiyuan |
| author_facet | Chen, Qiyuan |
| contents | The main contribution of this note is to establish a framework to extend results of tensor functions over specific field to general field. As a consequence of this framework, we extend the existing work to more general settings: \emph{(1)} slice rank is linearly bounded by geometric rank for any 3-tensors over any field. \emph{(2)} slice rank of any 3-tensors is quasi-supermultiplicative. As a consequence, the asymptotic slice rank exists for any 3-tensors. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_07173 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A base change framework for tensor functions Chen, Qiyuan Commutative Algebra Computational Complexity Combinatorics The main contribution of this note is to establish a framework to extend results of tensor functions over specific field to general field. As a consequence of this framework, we extend the existing work to more general settings: \emph{(1)} slice rank is linearly bounded by geometric rank for any 3-tensors over any field. \emph{(2)} slice rank of any 3-tensors is quasi-supermultiplicative. As a consequence, the asymptotic slice rank exists for any 3-tensors. |
| title | A base change framework for tensor functions |
| topic | Commutative Algebra Computational Complexity Combinatorics |
| url | https://arxiv.org/abs/2603.07173 |