## STNB2022 (35th edition)

### Inertia, conductor and $L$-function

Samuele Anni

#### Abstract

Following the talks of F. Bars Cortina and E. Lorenzo Garcia, we will explain how to describe the action of inertia on the étale cohomology for $\Delta_v$ regular curves. In particular we will related this to the computation of the conductor and of the $L$-factors of the associated $L$-function.