## Partially logarithmic ramification theory and characteristic cycles of rank 1 sheaves

### Abstract

The characteristic cycle of a constructible sheaf on a projective smooth algebraic variety is an algebraic cycle on the cotangent bundle that computes the Euler characteristic of the sheaf. In this talk, we consider a rank 1 sheaf on the variety. For a computation of the characteristic cycle of a rank 1 sheaf, we introduce a general theory called partially logarithmic ramification theory, and construct an algebraic cycle using several invariants measuring the ramification of the sheaf, which is compared with the characteristic cycle.