nLab
topological automorphic form

Contents

Idea

Topological automorphic forms are a generalization of topological modular forms: where the latter come with the moduli space of elliptic curves, topological automorphic forms are associated to a given Shimura variety. Moreover, just as topological modular forms refine to the tmf-spectrum representing the corresponding cohomology theory, so every Shimura variety induces a cohomology theory taftaf.

Properties

Chromatic pattern

chromatic level n=n = 123\geq 3
cohomology theory/spectrum E=E = KOTMFTAF
algebraic groupGL 1GL_1GL 2GL_2U(1,n1)U(1,n-1)
geometric objectmultiplicative groupelliptic curveShimura variety
FQFTsuperparticleheterotic superstring??

References

The definition is due to

An introductory survey is in

Lecture notes include

Revised on May 18, 2014 07:56:48 by Urs Schreiber (82.113.121.154)