Back to Algebraic Geometry Seminar: Fall 2012
Algebraic Geometry Seminar
Date: Tuesday, Oct 2, 2012
Time: 3:30PM - 4:30PM
Location: JTB 120
Takashi Kimura
Boston University
Title |
Power operations in inertial K-theory and some applications |
Abstract |
If X is a smooth variety with a proper action of an algebraic group G, its equivariant K-theory ring $K_G(X)$ possesses power (or Adams) operations (and associated lambda ring operations) which are compatible with the Chern character and Chern classes. But $K_G(X)$ is a subring of the equivariant K-theory $K_G(IX)$ of the inertial variety IX endowed with a so-called inertial product. The prototypical example of such an inertial K-theory ring is the K-theoretic version of the Chen-Ruan orbifold cohomology. We show that under certain conditions, the inertial K-theory ring admits inertial generalizations of power operations, Chern classes, and the Chern character. The power operations are then used to compare the virtual K-theory ring of P(1,2) and P(1,3) with the K-theory of a crepant resolution. This is joint work with with D. Edidin and T. Jarvis. |
Algebraic Geometry