Transfer and Norm for Finite Group Schemes
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866910085453709312 |
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| author | Karagiannis, Kostas Symonds, Peter |
| author_facet | Karagiannis, Kostas Symonds, Peter |
| contents | We develop the theory of transfer and norm maps for finite group schemes, extending classical results from finite group theory to a context where induction and restriction are not necessarily bi-adjoint. In the additive setting, we construct a transfer map for both modules and $\rm Ext $ groups and prove that its surjectivity characterizes relative projectivity, establishing a generalization of Higman's criterion. In the multiplicative setting, we define a relative norm map for algebras with a group scheme action. We compare this norm with other versions in the literature, proving that it coincides with Mumford's norm for finite morphisms and on fields is a power of the classical field norm. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_28501 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Transfer and Norm for Finite Group Schemes Karagiannis, Kostas Symonds, Peter Algebraic Geometry 14L15 We develop the theory of transfer and norm maps for finite group schemes, extending classical results from finite group theory to a context where induction and restriction are not necessarily bi-adjoint. In the additive setting, we construct a transfer map for both modules and $\rm Ext $ groups and prove that its surjectivity characterizes relative projectivity, establishing a generalization of Higman's criterion. In the multiplicative setting, we define a relative norm map for algebras with a group scheme action. We compare this norm with other versions in the literature, proving that it coincides with Mumford's norm for finite morphisms and on fields is a power of the classical field norm. |
| title | Transfer and Norm for Finite Group Schemes |
| topic | Algebraic Geometry 14L15 |
| url | https://arxiv.org/abs/2603.28501 |