A bound on the index of exponent-$4$ algebras in terms of the $u$-invariant
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2023
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| _version_ | 1866910324881358848 |
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| author | Becher, Karim Johannes Bingöl, Fatma Kader |
| author_facet | Becher, Karim Johannes Bingöl, Fatma Kader |
| contents | For a prime number $p$, an integer $e\geq 2$ and a field $F$ containing a primitive $p^e$-th root of unity, the index of central simple $F$-algebras of exponent $p^e$ is bounded in terms of the $p$-symbol length of $F$. For a nonreal field $F$ of characteristic different from $2$, the index of central simple algebras of exponent $4$ is bounded in terms of the $u$-invariant of $F$. Finally, a new construction for nonreal fields of $u$-invariant $6$ is presented. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2301_03378 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | A bound on the index of exponent-$4$ algebras in terms of the $u$-invariant Becher, Karim Johannes Bingöl, Fatma Kader Rings and Algebras 12E15, 16K20, 16K50 For a prime number $p$, an integer $e\geq 2$ and a field $F$ containing a primitive $p^e$-th root of unity, the index of central simple $F$-algebras of exponent $p^e$ is bounded in terms of the $p$-symbol length of $F$. For a nonreal field $F$ of characteristic different from $2$, the index of central simple algebras of exponent $4$ is bounded in terms of the $u$-invariant of $F$. Finally, a new construction for nonreal fields of $u$-invariant $6$ is presented. |
| title | A bound on the index of exponent-$4$ algebras in terms of the $u$-invariant |
| topic | Rings and Algebras 12E15, 16K20, 16K50 |
| url | https://arxiv.org/abs/2301.03378 |