Essential dimension of cohomology classes via valuation theory
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866916093485907968 |
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| author | Ofek, Danny Reichstein, Zinovy |
| author_facet | Ofek, Danny Reichstein, Zinovy |
| contents | We give a formula for the essential dimension of a cohomology class $α$ in $H^d(K, \mathbb{Q}_p/\mathbb{Z}_p (d))$ when $K$ is a strictly Henselian field. This formula is particularly explicit in the case, where $α$ is a Brauer class (for $d = 2$). As an application of our bound with $d = 3$, we study the essential dimension of exceptional groups by examining the image of the Rost invariant. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_08532 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Essential dimension of cohomology classes via valuation theory Ofek, Danny Reichstein, Zinovy Group Theory Commutative Algebra K-Theory and Homology 12G05, 12J20, 16K50, 19C30 We give a formula for the essential dimension of a cohomology class $α$ in $H^d(K, \mathbb{Q}_p/\mathbb{Z}_p (d))$ when $K$ is a strictly Henselian field. This formula is particularly explicit in the case, where $α$ is a Brauer class (for $d = 2$). As an application of our bound with $d = 3$, we study the essential dimension of exceptional groups by examining the image of the Rost invariant. |
| title | Essential dimension of cohomology classes via valuation theory |
| topic | Group Theory Commutative Algebra K-Theory and Homology 12G05, 12J20, 16K50, 19C30 |
| url | https://arxiv.org/abs/2401.08532 |