On Generalised Albert Forms over Discretely Valued Fields
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866916216420958208 |
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| author | Lorenz, Nico |
| author_facet | Lorenz, Nico |
| contents | For a discrete valuation ring $R$ with quotient field $K$ and residue field $F$ both of characteristic not 2, we study low-dimensional quadratic forms with Witt class in the $n$-th power of the fundamental ideal of $F$ resp. $K$ and point out connections between forms over these fields. We analyse the minimal number of Pfister forms such that a given form is Witt equivalent to the sum of these and study forms congruent modulo a higher power of the fundamental ideal towards similarity. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_02040 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On Generalised Albert Forms over Discretely Valued Fields Lorenz, Nico Number Theory 11E81, 12J10 For a discrete valuation ring $R$ with quotient field $K$ and residue field $F$ both of characteristic not 2, we study low-dimensional quadratic forms with Witt class in the $n$-th power of the fundamental ideal of $F$ resp. $K$ and point out connections between forms over these fields. We analyse the minimal number of Pfister forms such that a given form is Witt equivalent to the sum of these and study forms congruent modulo a higher power of the fundamental ideal towards similarity. |
| title | On Generalised Albert Forms over Discretely Valued Fields |
| topic | Number Theory 11E81, 12J10 |
| url | https://arxiv.org/abs/2403.02040 |