PSU Mark
Eberly College of Science Mathematics Department

Meeting Details

For more information about this meeting, contact Robert Vaughan.

Title:Test ideals via alterations
Seminar:Algebra and Number Theory Seminar
Speaker:Karl Schwede, Penn State University
Abstract:
Given a ring of equal characteristic p > 0, one can associate an ideal called the "test ideal" which captures informations about the singularities of Spec R. It has been known for about 2 decades that this ideal is closely related to the "multiplier ideal", an important tool for measuring singularities in complex algebraic geometry. While the multiplier ideal is most often defined via a resolution of singularities, the test ideal has historically been defined by studying the action of Frobenius on the ring. In particular, while the connection between these ideals was known, the underlying reason for the connection was a mystery. In this talk I give a description of an ideal, constructed via de Jong's alterations, which coincides with the test ideal in characteristic p and coincides with the multiplier ideal in characteristic 0. Finally, I will discuss some connections between these ideas and open questions in mixed characteristic. This is joint work with Manuel Blickle and Kevin Tucker.

Room Reservation Information

Room Number:MB106
Date:02 / 03 / 2011
Time:11:15am - 12:05pm