On Composition of Torsors

Mathieu Florence; Diego Izquierdo; Giancarlo Lucchini Arteche

doi:10.1093/imrn/rnad068

On Composition of Torsors

Mathieu Florence
, Diego Izquierdo
, Giancarlo Lucchini Arteche

Sorbonne Université
University of Chile

Résultats de recherche: Contribution à un journal › Article › Revue par des pairs

Résumé

Let K be a field, let X be a connected smooth K-scheme, and let G, H be two smooth connected K-group schemes. Given Y → X a G-torsor and Z → Y an H-torsor, we study whether one can find an extension E of G by H so that the composite Z → X is an E-torsor. We give both positive and negative results, depending on the nature of the groups G and H.

langue originale	Anglais
Pages (de - à)	16930-16956
Nombre de pages	27
journal	International Mathematics Research Notices
Volume	2023
Numéro de publication	19
Les DOIs	https://doi.org/10.1093/imrn/rnad068
état	Publié - 1 oct. 2023

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10.1093/imrn/rnad068

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title = "On Composition of Torsors",

abstract = "Let K be a field, let X be a connected smooth K-scheme, and let G, H be two smooth connected K-group schemes. Given Y → X a G-torsor and Z → Y an H-torsor, we study whether one can find an extension E of G by H so that the composite Z → X is an E-torsor. We give both positive and negative results, depending on the nature of the groups G and H.",

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N2 - Let K be a field, let X be a connected smooth K-scheme, and let G, H be two smooth connected K-group schemes. Given Y → X a G-torsor and Z → Y an H-torsor, we study whether one can find an extension E of G by H so that the composite Z → X is an E-torsor. We give both positive and negative results, depending on the nature of the groups G and H.

AB - Let K be a field, let X be a connected smooth K-scheme, and let G, H be two smooth connected K-group schemes. Given Y → X a G-torsor and Z → Y an H-torsor, we study whether one can find an extension E of G by H so that the composite Z → X is an E-torsor. We give both positive and negative results, depending on the nature of the groups G and H.

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DO - 10.1093/imrn/rnad068

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On Composition of Torsors

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