On quaternionic rigid meromorphic cocyles

2020/09/10 by Lennart Gehrmann, Gehrmann, Lennart
Mathematics · #FOS: Mathematics #Number Theory (math.NT) #math.NT

paper · pdf · doi:10.48550/arxiv.2009.04957

10 pages, to appear in Math. Res. Lett

arxiv created 2021/06/30 · arxiv updated 2021/07/01

Abstract

Recently, Darmon and Vonk initiated the theory of rigid meromorphic cocycles for the group SL₂(ℤ[1/p]). One of their major results is the algebraicity of the divisor associated to such a cocycle. We generalize the result to the setting of \mathfrakp-arithmetic subgroups of inner forms of SL₂ over arbitrary number fields. The method of proof differs from the one of Darmon and Vonk. Their proof relies on an explicit description of the cohomology via modular symbols and continued fractions, whereas our main tool is Bieri-Eckmann duality for arithmetic groups.

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