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arXiv · 2603.28501

Transfer and Norm for Finite Group Schemes

Kostas Karagiannis·Peter Symonds
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Abstract

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.

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Kostas Karagiannis, Peter Symonds. 2026-06-18. Transfer and Norm for Finite Group Schemes. https://arxiv.org/abs/2603.28501

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