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Pré-Publication, Document De Travail Année : 2024

The norm functor over schemes

Résumé

We construct a globalization of Ferrand's norm functor over rings which generalizes it to the setting of a finite locally free morphism of schemes T → S of constant rank. It sends quasi-coherent modules over T to quasicoherent modules over S. These functors restrict to the category of quasicoherent algebras. We also assemble these functors into a norm morphism from the stack of quasi-coherent modules over a finite locally free of constant rank extension of the base scheme into the stack of quasi-coherent modules. This morphism also restricts to the analogous stacks of algebras. Restricting our attention to finite étale covers, we give a cohomological description of the norm morphism in terms of the Segre embedding. Using this cohomological description, we show that the norm gives an equivalence of stacks of algebras A 2 1 ≡ D 2 , akin to the result shown in The Book of Involutions.
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Dates et versions

hal-04399243 , version 1 (17-01-2024)
hal-04399243 , version 2 (23-01-2024)

Identifiants

  • HAL Id : hal-04399243 , version 2

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Philippe Gille, Erhard Neher, Cameron Ruether. The norm functor over schemes. 2024. ⟨hal-04399243v2⟩
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