Let be a nowhere vanishing holomorphic function on the Drinfeld space of dimension , where . The logarithm of its absolute value may be regarded as an affine function on the attached Bruhat–Tits building . Generalizing a construction of van der Put in case , we relate the group of such with the group of integer-valued harmonic 1-cochains on . This also gives rise to a natural -structure on the first (-adic or de Rham) cohomology of .
"Invertible functions on nonarchimedean symmetric spaces." Algebra Number Theory 14 (9) 2481 - 2504, 2020. https://doi.org/10.2140/ant.2020.14.2481