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We show that any infinite algebraic subgroup of the plane Cremona group over a perfect field is contained in a maximal algebraic subgroup of the plane Cremona group. We classify the maximal groups, and their subgroups of rational points, up to conjugacy by a birational map. Comment: With a Corrigendum closing a gap in the classification
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Schneider, J., & Zimmermann, S. (2021). Algebraic subgroups of the plane Cremona group over a perfect field. Épijournal de Géométrie Algébrique, Volume 5. https://doi.org/10.46298/epiga.2021.6715
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