Symbol length in positive characteristic
Fuente:
arXiv
Salvato in:
| Autore principale: | |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2023
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866910307994042368 |
|---|---|
| author | Bingöl, Fatma Kader |
| author_facet | Bingöl, Fatma Kader |
| contents | We show that any central simple algebra of exponent $p$ in prime characteristic $p$ that is split by a $p$-extension of degree $p^n$ is Brauer equivalent to a tensor product of $2\cdot p^{n-1}-1$ cyclic algebras of degree $p$. If $p=2$ and $n\geq3$, we improve this result by showing that such an algebra is Brauer equivalent to a tensor product of $5\cdot2^{n-3}-1$ quaternion algebras. Furthermore, we provide new proofs for some bounds on the minimum number of cyclic algebras of degree $p$ that is needed to represent Brauer classes of central simple algebras of exponent $p$ in prime characteristic $p$, which have previously been obtained by different methods. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2307_06650 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Symbol length in positive characteristic Bingöl, Fatma Kader Rings and Algebras 16K20, 13A35 We show that any central simple algebra of exponent $p$ in prime characteristic $p$ that is split by a $p$-extension of degree $p^n$ is Brauer equivalent to a tensor product of $2\cdot p^{n-1}-1$ cyclic algebras of degree $p$. If $p=2$ and $n\geq3$, we improve this result by showing that such an algebra is Brauer equivalent to a tensor product of $5\cdot2^{n-3}-1$ quaternion algebras. Furthermore, we provide new proofs for some bounds on the minimum number of cyclic algebras of degree $p$ that is needed to represent Brauer classes of central simple algebras of exponent $p$ in prime characteristic $p$, which have previously been obtained by different methods. |
| title | Symbol length in positive characteristic |
| topic | Rings and Algebras 16K20, 13A35 |
| url | https://arxiv.org/abs/2307.06650 |