Strong u-invariant and Period-Index bound for complete ultrametric fields
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866909259276484608 |
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| author | Mandal, Shilpi |
| author_facet | Mandal, Shilpi |
| contents | Let $k$ be a complete ultrametric valued field. Let u($k$) (resp. u_s($k$)) denote the u-invariant (resp. the strong u-invariant) of $k$. We give a description of this invariant for $k$ in terms of the u-invariant (resp. the strong u-invariant) of its residue field. Let $C$ be a curve over $k$ and $F$ = $k(C)$. We prove similar results for the u-invariant of $F$. For $l$ a prime away from the characteristic of the residue field of $k$, we obtain bounds for the Brauer-$l$-dimensions of $k$ and $F$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_12169 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Strong u-invariant and Period-Index bound for complete ultrametric fields Mandal, Shilpi Algebraic Geometry Number Theory Let $k$ be a complete ultrametric valued field. Let u($k$) (resp. u_s($k$)) denote the u-invariant (resp. the strong u-invariant) of $k$. We give a description of this invariant for $k$ in terms of the u-invariant (resp. the strong u-invariant) of its residue field. Let $C$ be a curve over $k$ and $F$ = $k(C)$. We prove similar results for the u-invariant of $F$. For $l$ a prime away from the characteristic of the residue field of $k$, we obtain bounds for the Brauer-$l$-dimensions of $k$ and $F$. |
| title | Strong u-invariant and Period-Index bound for complete ultrametric fields |
| topic | Algebraic Geometry Number Theory |
| url | https://arxiv.org/abs/2407.12169 |