Quadratic conductor formulas
Abatract: Motivic methods allow replacing the ring of integers by the Grothendieck-Witt ring of a field to get refined versions to formulas in algebraic geometry. We will review Milnor's number formula for complex degenerations and its analogues in algebraic geometry. We will then report on a work by Levine, Pepin Lehalleur and Srinivas, computing the motivic Euler characteristic for projective hypersurfaces and obtaining a refined conductor formula in quadratic forms. We will describe how to compute the motivic Euler characteristic of the motivic nearby cycles functor to obtain a quadratic conductor formula for a more general degeneration with several isolated singularities, refining Milnor's formula.
ID: 821 8253 0518