The A1A_1 conjecture for dihedral quasi-Frobenius configurations

Let (C<G)(C < G) be a definable, connected, quasi-Frobenius pair of finite Morley rank. Suppose that GG is U2U_2^\perp with involutions, and that the configuration is dihedral. The A1A_1 conjecture. Then

GPGL2(K).G \simeq \operatorname{PGL}_2(\mathbb{K}).

This conjecture predicts that dihedral quasi-Frobenius configurations arise from the algebraic group of type A1A_1. The source describes this as expected, while no resolution is supplied here.

Sources & referencesView supporting material

Primary source

Tuna Altinel, Luis Jaime Corredor and Adrien Deloro, “On quasi-Frobenius pairs of finite Morley rank”, arXiv:2305.00830 (2023).

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