Degree bounds for syzygies of invariants

Suppose that G is a linearly reductive group. Good degree bounds for generators of invariant rings were given in (Proc. Amer. Math. Soc. 129 (4) (2001) 955). Here we study minimal free resolutions of invariant rings. For finite linearly reductive groups G it was recently shown in (Adv. Math. 156 (1) (2000) 23, Electron Res. Announc. Amer. Math. Soc. 7 (2001) 5, Adv. Math. 172 (2002) 151) that rings of invariants are generated in degree at most the group order |G|. In characteristic 0 this degree bound is a classical result by Emmy Noether (see Math. Ann. 77 (1916) 89). Given an invariant ring of a finite linearly reductive group G, we prove that the ideal of relations of a minimal set of generators is generated in degree at most ?2|G|.