Characteristic cycle of a rank 1 sheaf on a surface: research announcement (Algebraic Number Theory and Related Topics 2014)

"Algebraic Number Theory and Related Topics 2014". December 1～5, 2014. edited by Takeshi Tsuji, Hiroki Takahashi and Yuichiro Hoshi. The papers presented in this volume of RIMS Kôkyûroku Bessatsu are in final form and refereed.This is a research announcement about a study of characteristic cycle of a rank 1 sheaf on a surface on which I am writing a paper. In this announcement, we construct a canonical lifting of Kato's logarithmic characteristic cycle on the cotangent bundle of the surface. As a corollary, an index formula computing the Euler characteristic of the sheaf is yielded by the canonical lifting