The Shimura curve of discriminant 15 and topological automorphic forms

2013/01/15 by Lawson, Tyler
#11F23 #11G18 #14G35 #55P42 (primary) #55P43 (secondary) #Algebraic Topology (math.AT) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1301.3233

Abstract

We find defining equations for the Shimura curve of discriminant 15 over Z[1/15]. We then determine the graded ring of automorphic forms over the 2-adic integers, as well as the higher cohomology. We apply this to calculate the homotopy groups of a spectrum of "topological automorphic forms" associated to this curve, as well as one associated to a quotient by an Atkin-Lehner involution.

Related

• Automorphic forms and cohomology theories on Shimura curves of small discriminant
• On the group of automorphisms of Shimura curves and applications
• Computing automorphic forms on Shimura curves over fields with arbitrary class number
• Shimura curve Atkin--Lehner quotients of genus at most two
• Topological automorphic forms