A bound on the index of exponent-$4$ algebras in terms of the $u$-invariant
| Autor: | Becher, Karim Johannes, Bingöl, Fatma Kader |
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| Rok vydání: | 2023 |
| Předmět: | |
| Zdroj: | New York J. Math. 29 (2023) 1273-1286 |
| Druh dokumentu: | Working Paper |
| Popis: | 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. Comment: 12 pages |
| Databáze: | arXiv |
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