Classifying torsors of tori with Brauer groups

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This is a Quantitative Study study.

Alexander Duncan; Pankaj Singh

doi:10.48550/arxiv.2505.10386

May 15, 2025Open Access

Classifying torsors of tori with Brauer groups

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Key Points

This research provides a general framework for classifying torsors using Brauer groups, enhancing our understanding of algebraic tori.
It establishes connections to del Pezzo surfaces of degree 6, generalizing existing theories to a broader class of retract rational tori.
Utilizing Mackey functors, the study offers a new approach to understanding torsors of algebraic structures within finite fields.
The findings may significantly impact future research on rational tori and their classifications through algebraic methods.

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Implication

This framework classifies torsors in algebraic tori through Brauer groups of field extensions, suggesting new connections.

Abstract

Using Mackey functors, we provide a general framework for classifying torsors of algebraic tori in terms of Brauer groups of finite field extensions of the base field. This generalizes Blunk's description of the tori associated to del Pezzo surfaces of degree 6 to all retract rational tori, essentially the largest class for which this is possible.

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Cite This Study

Duncan et al. (2025) studied this question.

synapsesocial.com/papers/68f163c79903599108abcb63 https://doi.org/10.48550/arxiv.2505.10386

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Classifying torsors of tori with Brauer groups

Key Points

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Implication

Abstract

Discussion

Cite This Study

Classifying torsors of tori with Brauer groups

Key Points

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Implication

Abstract

Discussion

Cite This Study

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