Character stacks are PORC count

Abstract

We compute the number of points over finite fields of the character stack associated to a compact surface group and a reductive group with connected centre. We find that the answer is a Polynomial On Residue Classes (PORC). The key ingredients in the proof are Lusztig's Jordan decomposition of complex characters of finite reductive groups and Deriziotis's results on their genus numbers . As a consequence of our main theorem, we obtain an expression for the E-polynomial of the character stack.