Abstract:

The characteristic cycle of a constructible sheaf on a smooth variety is an algebraic cycle of the cotangent bundle which is defined by T. Saito in 2015 and which computes the Euler characteristic of the sheaf as an intersection number. 

The characteristic cycle has much to do with the ramification of the sheaf and is expected to be comuted in terms of the ramification theory of the sheaf.

In this talk, I will talk about a computation of the characteristic cycle of a rank 1 sheaf using ramification theory. 

I will introduce a result for a rank 1 sheaf on a surface and I would like to mention a recent small development for a rank 1 sheaf in Artin-Shreier case.