F-singularities and Frobenius closure of ideals

Date: 
Monday, September 9, 2019 - 4:00pm
Location: 
110 Math Science Building
Speaker: 
Kyle Maddox

F-singularities and Frobenius closure of ideals
 

Abstract:

 

The canonical Frobenius map defined for any prime characteristic ring can both reveal and obscure an incredible amount of data about the ring. In this talk, we will first discuss a closure operation (Frobenius closure) on ideals defined in terms of the Frobenius map, then outline a similar map (a Frobenius action) on local cohomology which can be used to define a variety of singularities in prime characteristic, and finally discuss connections between the Frobenius closure of parameter ideals and the Frobenius action on local cohomology.

Event Type: