  In this paper, proof of the {\it Kurlberg-Rudnick supremum conjecture} for
the quantum Hannay-Berry model is presented. This conjecture was stated in P.
Kurlberg's lectures at Bologna 2001 and Tel-Aviv 2003. The proof is a primer
application of a fundamental solution: all the Hecke eigenfunctions of the
quantum system are constructed. The main tool in our construction is the
categorification of the compatible system of realizations of the Heisenberg
representation over a finite field. This enables us to construct certain
"perverse sheaves" that stands motivically prior to the Hecke eigenfunctions.
