Wild division algebras over Laurent series fields

Abstract

In previous papers [HoEis], [Ho2000] we found neat Picard modular surfaces with abelian minimal model and, conversely, a divisor criterion on abelian surfaces A for such a situation. For the corresponding ball lattices $\Gamma$ we prove dimension formulas for modular forms depending only on the intersection graph of the image on A of the compactification divisor of the $\Gamma$-quotient surface.