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.
From: Kostas Karagiannis [view email]
[v1]
Mon, 30 Mar 2026 14:38:02 UTC (120 KB)
[v2]
Thu, 18 Jun 2026 15:19:45 UTC (121 KB)
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