Classification of Equivariant Line Bundles on the Drinfeld Upper Half Plane

Georg Linden

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arXiv · 2510.10330

Classification of Equivariant Line Bundles on the Drinfeld Upper Half Plane

Georg Linden

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Abstract

We explicitly determine the group of isomorphism classes of equivariant line bundles on the non-archimedean Drinfeld upper half plane for $\mathrm{GL}_2(F)$, for its subgroups of matrices whose determinant has even (respectively trivial) valuation, and for $\mathrm{GL}_2(\mathcal{O}_F)$. Our results extend a recent classification of torsion equivariant line bundles with connection due to Ardakov and Wadsley, but we use a different approach. A crucial ingredient is a construction due to Van der Put which relates invertible analytic functions on the Drinfeld upper half plane to currents on the Bruhat-Tits tree. Another tool we use is condensed group cohomology.

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Georg Linden. 2025-10-11. Classification of Equivariant Line Bundles on the Drinfeld Upper Half Plane. https://arxiv.org/abs/2510.10330

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