#### Vol. 311, No. 1, 2021

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Embeddings of maximal tori in groups of type $F_4$

### Andrew Fiori and Federico Scavia

Vol. 311 (2021), No. 1, 53–88
DOI: 10.2140/pjm.2021.311.53
##### Abstract

We classify maximal tori in groups of type ${F}_{4}$ over a local or global field of characteristic different from $2$ and $3$. We prove a local-global principle for embeddings of maximal tori in groups of type ${F}_{4}$.

##### Keywords
maximal tori, Jordan algebras, exceptional groups, quadratic forms
##### Mathematical Subject Classification 2010
Primary: 20G30, 20G41
Secondary: 11E12
##### Milestones
Revised: 14 November 2020
Accepted: 14 January 2021
Published: 17 March 2021
##### Authors
 Andrew Fiori Department of Mathematics and Computer Science University of Lethbridge Lethbridge, AB Canada Federico Scavia Department of Mathematics University of British Columbia Vancouver, BC Canada