- Series
- Algebra Seminar
- Time
- Monday, March 25, 2019 - 12:50pm for 1 hour (actually 50 minutes)
- Location
- Skiles 005
- Speaker
- Ben Blum-Smith – NYU
- Organizer
- Josephine Yu
If a finite group G acts on a Cohen-Macaulay ring A, and the order of G is a unit in A, then the invariant ring AG is Cohen-Macaulay as well, by the Hochster-Eagon theorem. On the other hand, if the order of G is not a unit in A then the Cohen-Macaulayness of AG is a delicate question that has attracted research attention over the last several decades, with answers in several special cases but little general theory. In this talk we show that the statement that AG is Cohen-Macaulay is equivalent to a statement quantified over the inertia groups for the action of GonAactingonstricthenselizationsofappropriatelocalizationsofA$. In a case of long-standing interest—a permutation group acting on a polynomial ring—we show how this can be applied to find an obstruction to Cohen-Macaulayness that allows us to completely characterize the permutation groups whose invariant ring is Cohen-Macaulay regardless of the ground field. This is joint work with Sophie Marques.