Automorphic forms and cohomology theories on Shimura curves of small discriminant

Abstract

We compute the homotopy groups of spectra associated by a theorem of Lurie to the Shimura curves of discriminants 6, 10, and 14, beginning with a computation of integral rings of automorphic forms on these curves. As an application, we find that a generalized truncated Brown-Peterson spectrum BP<2> is an E_\infty ring spectrum at the prime 3.

arXiv comment46 pages, 3 figures. Updated version.

References in corpus (1)

• Topological automorphic forms on U(1,1)

Cited by in corpus (1)

• Realizing Families of Landweber Exact Homology Theories