Abstract

We use the machinery of A1-homotopy theory to study the geometric ramification theory. We define the quadratic Artin conductor for a motivic spectrum on a smooth proper curve and obtain a quadratic refinement of the classical Grothendieck-Ogg-Shafarevich formula. Then we use the non-acyclicity class to formulate a quadratic conductor formula. In some sense, we obtain a quadratic version of Bloch’s conductor formula. This is joint work with Fangzhou Jin.