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

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Pages (from-to)	16930-16956
Number of pages	27
Journal	International Mathematics Research Notices
Volume	2023
Issue number	19
DOIs	https://doi.org/10.1093/imrn/rnad068
Publication status	Published - 1 Oct 2023

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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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PY - 2023/10/1

Y1 - 2023/10/1

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.

UR - https://www.scopus.com/pages/publications/85175187452

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DO - 10.1093/imrn/rnad068

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EP - 16956

JO - International Mathematics Research Notices

JF - International Mathematics Research Notices

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ER -

On Composition of Torsors

Abstract

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