Abstract
The Lubin-Tate moduli space Xrig0 is a p-adic analytic open unit polydisc which parametrizes deformations of a formal group H0 of finite height defined over an algebraically closed field of characteristic p. It is known that the natural action of the automorphism group Aut(H0) on Xrig0 gives rise to locally analytic representations on the topological duals of the spaces H0(Xrig0 , (ℳs0 )rig) of global sections of certain equivariant vector bundles (ℳs0 )rig over Xrig0 . In this article, we show that this result holds in greater generality. On the one hand, we work in the setting of deformations of formal modules over the valuation ring of a finite extension of ℚp. On the other hand, we also treat the case of representations arising from the vector bundles (ℳsm )rig over the deformation spaces Xrigm with Drinfeld level-m-structures. Finally, we determine the space of locally finite vectors in H0(Xrigm , (ℳsm )rig). Essentially, all locally finite vectors arise from the global sections of invertible sheaves over the projective space via pullback along the Gross-Hopkins period map.
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Sheth, M. Locally analytic representations in the étale coverings of the Lubin-Tate moduli space. Isr. J. Math. 239, 369–433 (2020). https://doi.org/10.1007/s11856-020-2059-z
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DOI: https://doi.org/10.1007/s11856-020-2059-z