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2020 Invertible functions on nonarchimedean symmetric spaces
Ernst-Ulrich Gekeler
Algebra Number Theory 14(9): 2481-2504 (2020). DOI: 10.2140/ant.2020.14.2481

Abstract

Let u be a nowhere vanishing holomorphic function on the Drinfeld space Ωr of dimension r1, where r2. The logarithm logq|u| of its absolute value may be regarded as an affine function on the attached Bruhat–Tits building 𝒯r. Generalizing a construction of van der Put in case r=2, we relate the group 𝒪(Ωr) of such u with the group H(𝒯r,) of integer-valued harmonic 1-cochains on 𝒯r. This also gives rise to a natural -structure on the first (-adic or de Rham) cohomology of Ωr.

Citation

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Ernst-Ulrich Gekeler. "Invertible functions on nonarchimedean symmetric spaces." Algebra Number Theory 14 (9) 2481 - 2504, 2020. https://doi.org/10.2140/ant.2020.14.2481

Information

Received: 16 September 2019; Revised: 30 March 2020; Accepted: 11 May 2020; Published: 2020
First available in Project Euclid: 12 November 2020

MathSciNet: MR4172713
Digital Object Identifier: 10.2140/ant.2020.14.2481

Subjects:
Primary: 32P05
Secondary: 11F23, 11F85, 32C30, 32C36

Rights: Copyright © 2020 Mathematical Sciences Publishers

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Vol.14 • No. 9 • 2020
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