Higher Chern classes in Iwasawa theory

Chern Classes for Twisted K-theory

We define a total Chern class map for the K-theory of a variety X twisted by a central simple algebra A. This includes defining a suitable notion of the motivic cohomology of X twisted by A to serve as the target for such a map. Our twisted motivic groups turn out to be different than those defined and studied by Kahn and Levine.

Chern Classes for Twisted K-theory

We define a total Chern class map for the K-theory of a variety X twisted by a central simple algebra A. This includes defining a suitable notion of the motivic cohomology of X twisted by A to serve as the target for such a map. Our twisted motivic groups turn out to be different than those defined and studied by Kahn and Levine.

Characteristic Classes, Chern Classes and Applications to Intersection Theory

This is a report for my summer REU program at the University of Chicago, 2014. I would like to acknowledge my mentor Sean Howe in this program for his generous guidance on learning the subject and writing this article, Professor J.P. May who runs this REU program successfully and made my wonderful experience possible, and Professor M. Yan who has encouraged me ever since my first year in colleg...

Introduction to Iwasawa Theory

Stringy Chern classes

Work of Dixon, Harvey, Vafa and Witten in the 80’s ([DHVW85]) introduced a notion of Euler characteristic (for quotients of a torus by a finite group) which became known as the physicist’s orbifold Euler number. In the 90’s V. Batyrev introduced a notion of stringy Euler number ([Bat99b]) for ‘arbitrary Kawamata log-terminal pairs’, proving that this number agrees with the physicist’s orbifold ...