Topological automorphic forms on U(1,1)

TL;DR

This paper explicitly describes the homotopy type and groups of spectra of topological automorphic forms related to a specific unitary group, revealing their close relation to the well-studied spectrum TMF.

Contribution

It provides explicit descriptions of the homotopy type and groups of TAF spectra for the (1,1) unitary case, connecting them to TMF.

Findings

Homotopy groups of TAF spectra are explicitly computed.

TAF spectra are closely related to TMF in quasi-split cases.

Homotopy types of these spectra are characterized explicitly.

Abstract

The homotopy type and homotopy groups of some spectra TAF of topological automorphic forms associated to a unitary similitude group GU of type (1,1) are explicitly described in quasi-split cases. The spectrum TAF is shown to be closely related to the spectrum TMF in these cases, and homotopy groups of some of these spectra are explicitly computed.