C2-Cofiniteness of Cyclic-Orbifold Models

We prove an orbifold conjecture for conformal field theory with a solvable automorphism group. Namely, we show that if V is a -cofinite simple vertex operator algebra and G is a finite solvable automorphism group of V, then the fixed point vertex operator subalgebra is also -cofinite, where -cofiniteness is equivalent to the condition that V has only finitely many isomorphism classes of simple V-modules (including weak modules) and all finitely generated V-modules have composition series. This result offers a mathematically rigorous background to orbifold theories with solvable automorphism groups.