#### Vol. 14, No. 9, 2020

 Recent Issues
 The Journal About the Journal Editorial Board Editors’ Interests Subscriptions Submission Guidelines Submission Form Policies for Authors Ethics Statement ISSN: 1944-7833 (e-only) ISSN: 1937-0652 (print) Author Index To Appear Other MSP Journals
Invertible functions on nonarchimedean symmetric spaces

### Ernst-Ulrich Gekeler

Vol. 14 (2020), No. 9, 2481–2504
##### Abstract

Let $u$ be a nowhere vanishing holomorphic function on the Drinfeld space ${\Omega }^{r}$ of dimension $r-1$, where $r\ge 2$. The logarithm ${log}_{q}|u|$ of its absolute value may be regarded as an affine function on the attached Bruhat–Tits building ${\mathsc{ℬ}\mathsc{𝒯}}^{r}$. Generalizing a construction of van der Put in case $r=2$, we relate the group $\mathsc{𝒪}{\left({\Omega }^{r}\right)}^{\ast }$ of such $u$ with the group $\mathbf{H}\left({\mathsc{ℬ}\mathsc{𝒯}}^{r},ℤ\right)$ of integer-valued harmonic 1-cochains on ${\mathsc{ℬ}\mathsc{𝒯}}^{r}$. This also gives rise to a natural $ℤ$-structure on the first ($\ell$-adic or de Rham) cohomology of ${\Omega }^{r}$.

However, your active subscription may be available on Project Euclid at
https://projecteuclid.org/ant

We have not been able to recognize your IP address 3.219.31.204 as that of a subscriber to this journal.
Online access to the content of recent issues is by subscription, or purchase of single articles.

or by using our contact form.