Brauer $p$-dimension and Kato's Swan Conductor
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866916422799589376 |
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| author | Zhao, Yizhen |
| author_facet | Zhao, Yizhen |
| contents | We use Kato's Swan conductor to study the Brauer $p$-dimension of fields of characteristic $p>0$. We mainly investigate two types of fields: henselian discretely valued fields and semi-global fields. While investigating the Brauer $p$-dimension of semi-global fields, we use a Gersten-type sequence to analyse the ramification behavior of a Brauer class in a $2$-dimensional regular local ring. Using this result, we give a partial result on the Brauer $p$-dimension of function fields of algebraic curves over $\bar{k}((t))$ with good reduction. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_02926 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Brauer $p$-dimension and Kato's Swan Conductor Zhao, Yizhen Algebraic Geometry Number Theory Rings and Algebras We use Kato's Swan conductor to study the Brauer $p$-dimension of fields of characteristic $p>0$. We mainly investigate two types of fields: henselian discretely valued fields and semi-global fields. While investigating the Brauer $p$-dimension of semi-global fields, we use a Gersten-type sequence to analyse the ramification behavior of a Brauer class in a $2$-dimensional regular local ring. Using this result, we give a partial result on the Brauer $p$-dimension of function fields of algebraic curves over $\bar{k}((t))$ with good reduction. |
| title | Brauer $p$-dimension and Kato's Swan Conductor |
| topic | Algebraic Geometry Number Theory Rings and Algebras |
| url | https://arxiv.org/abs/2410.02926 |