Seminar

Rings of polynomial invariants of finite group actions are among the most classical objects in commutative algebra. There are many beautiful theorems ensuring that the invariant ring has good properties when the order of group is invertible, but if the order of the group is not a unit (i.e., is divisible by the characteristic of the ground field), many of these properties become more subtle. One key issue is that the ring of invariants may fail to be a direct summand of the polynomial ring. In this talk, we will review some of these subtleties, and provide a generalization of a result of Singh on this direct summand property for rings of modular invariants.